Edit: As of at least 6-15-2022, I have adopted the view that the civil magistrate is in fact bound to punish 1st-table offenses, punishing blasphemy with death and as for idolatry, punishing public atheism and polytheism at the very least with the same (I am still unsure how exactly the Reformed view civil punishment of idolatry works). Warrant for such can be found, I believe, most strongly in Job 31:28, Daniel 3:29 and book X of Plato's Laws. I believe there is some controversy over how this is to exactly work out among the Reformed, but I largely follow Turretin, Junius and Rutherford with exception to the Sabbath, which I believe to have been purely ceremonial. Also apostasy in and of itself must not be punished and heresy must be carefully defined so that all Christian denominations are allowed (see here https://twitter.com/brandoncorley99/status/1531810854320017408?s=21&t=J9yrdwe_4s4-flp4zSZILw Blackwood's treatise as a whole, which Ive read through a few times is somehwhat confusing as to what exactly he is advocating for and I question whether it is consistent with itself; and Im not the only one who thinks this, see pg. 966 here: https://www.jstor.org/stable/pdf/3020858.pdf?refreqid=excelsior%3Af5f05711be66429487803e3bd6c673c3&ab_segments=&origin= but I think that we can form a somewhat coherent picture and see that his main concern, being a Baptist, was to prevent orthodox Christians who disagree on certain matters from being charged with heresy and punished, which certainly I would absolutely and strongly agree with. I think a more well thought out and consistent system is already found in Reformers like Turretin and Junius, which it would seem Baptists like John Gill and John Tombes agreed with (although Tombes being more of an antipaedobaptist) Other Baptists who I believe might be considered friendly to this "Magisterial Baptist" position include William Kiffen, John Spilsbury, Thomas Patient, Henry Jessey, Hanserd Knollys, and Henry Lawrence. I think that punishment-wise, John Cotton's laws are near perfect (https://reformed.org/ethics/an-abstract-of-the-laws-of-new-england-as-they-are-now-established-by-john-cotton/), just with exception to punishing for the Sababth and I don't think forcing of a maid must absolutely not be punished with death, but perhaps it is safer that it is not. Nevertheless, it is clear that Blackwood is advocating a clearly Christian concept of religious liberty. I would personally advocate for a general protestant state (and thus would side with Blackwood's comments against Catholics over against the parts in which he seems to support them).
I have recently been reading Samuel Rutherford's A Free Disputation Against Pretended Liberty of Conscience. I regard Rutherford as one of the best writers on Reformed political theology and natural law and therefore one of the best sources to go to for the Reformers' view of general equity.
Much of his disputation concerns his argument that the civil Magistrate ought to punish idolatry/heresy/blasphemy. I'm afraid I have to disagree with Rutherford here, as I will return to this matter later, but I want to recognize that he makes a very compelling argument. Rutherford takes on Roger Williams' "Bloody Tenet" in the book, and I believe rightly calls out many of Williams' arguments as logically fallacious and "anabaptistical" (a word I hope to use more often). I do not regard Roger Williams as an exemplary theologian at all (or even a genuine Baptist), but even though I disagree with Rutherford, he very clearly and cogently sets forth the Magisterially Reformed view of 2K theology. Rutherford is clear that the state cannot positively coerce men to believe and to be Christians, but they can and must negatively, punish heresy and blasphemy. Men's consciences are not bound to worship under this system and men are not coerced to convert by the sword (both things that Rutherford regards as wicked). Nevertheless, a state has the obligation to recognize the true God and to punish all worship that is contrary to Him, even though private opinions contrary to Christianity can be held. It is really more of a limiting of freedom of speech rather than of religious liberty, if that makes any sense.
Regarding the general equity of 2nd-table offenses (a topic I have been concentrating on, as evidenced by my recent posts), I have collected some citations that I will hopefully be adding to as I read on which reveal Rutherford's thought on this:
"if the Magistrate spare the life of a murderer, the watchmen are unfaithful"
Shortly and simply, it is clear that Rutherford here regards the death penalty for murder as a necessary punishment. A magistrate is unfaithful to the moral law of God if they allow a murderer to live. There are no exceptions. The natural, moral law demands the death of those who take the lives of others.
"It was the Magistates duty to take away their head for Sodomy, which certainly it was, and that by the very law of nature"
Another quote that very clearly shows that Rutherford regards the death penalty for Sodomy as part of the natural law. From what I can tell, this is pretty universal among the Reformed. In the context of this section, Rutherford is making a reductio ad absurdum in order to prove that idolatry should be punished. His argument would not work if his readers did not believe that it is absurd to claim that Sodomy ought not to be punished by death. He makes this exact same argument throughout his work, using other crimes like Adultery, Sorcery, and Murder in place of Sodomy. It was quite clear to him, as he expected it to be of others that Murder, Adultery, Sorcery, and Sodomy all ought to be punished by nothing less than the death penalty. If you claim to be "Confessional" in holding to 19.4 (To them also, as a body politic, He gave sundry judicial laws, which expired together with the State of that people; not obliging under any now, further than the general equity thereof may require), but do not understand "general equity" in the same way that those who wrote it understood it, you are not Confessional, you are a moral relativist whose conscience has been so seared that you regard the most grotesque Sodomy as a crime that God would have Magistrates suffer men to live after committing.
"The English divines do well observe that adultery is a capital crime to be punished by the judge, Gen. 38.24"
Another place where we can see Rutherford's understanding of general equity, along with the English divines, as requiring the death penalty for one of the very worse crimes of adultery. Genesis 38:24, which Rutherford cites says “About three months later Judah was told, “Your daughter-in-law, Tamar, has been acting like a prostitute, and now she is pregnant.” “Bring her out,” Judah said, “and let her be burned to death!””. This is a great observation given that this is prior to the giving of the Mosaic Law, clearly showing that the death penalty for adultery, as we have been saying, just like murder, is an immutable part of natural, moral law; but we don't absolutely need this verse to tell us this (except to correct our fallen notions), as it is quite evident from the light of nature and conscience.
He also makes an interesting argument, also followed by Junius, from Job 31:28, "this [idolatry] would also be an iniquity deserving punishment, for I would have denied God above" comparing it to Job 31:11 “For that [adultery] would be a disgrace; it would be an iniquity deserving punishment" to argue that if the adultery of 31:11 is spoken of as "deserving punishment" (apparently civil punishment. Lit. "punishable by judges"), then so too must 31:28 speaking of idolatry. I think this is a really good argument and I don't currently have a satisfying response to it. Though I still believe only second-table offenses should be punished, I would like to point out that I am unsure if Confessional Baptist theology absolutely demands this, as early Baptists certainly did not think that it did https://twitter.com/mpw1689/status/1514462960101433346?s=21&t=YmQr78tACCTZTWUuyA9zkQ as long as the Magistrate is not viewed as the Kingdom of God, nor is the common realm made sacred but instead is viewed simply as enforcing the law of nature, as on this position, part of the law of the common realm involves punishing worship contrary to the true God.
I do wonder then, whether a "Baptist Covenanter" position would be consistent with, if not even be the position of many framers of the 2LBCF. I do want to add that would I ever adopt this position, I do not at all see it as inconsistent with my rejection of Sabbatarianism, as if a Sabbath day is not a part of natural, moral law (as I argue is the case), then it simply need not be legislated against unlike adultery, murder, and idolatry and blasphemy on this position; I simply deny the premise that a weekly Sabbath principle is a part of the law of nature, along with the earliest church fathers.
Edit (8/7/22): In fact, to turn the tables, Joe Rigney has pointed out a major inconsistency for those who hold that (https://twitter.com/joe_rigney/status/1547715642559647749?s=21&t=SbvuW-o9fNakKu_lgnFHoQ):
1. The decalogue is the moral law
2. We ought not to enforce laws against idolatry/blasphemy/false worship
3. We ought to enforce the Sabbath
One who accepts these 3 positions inconsistently semi-bifurcates the two tables, arbitrarily choosing only one command from the first table to enforce. When one makes the distinction between internal coercion of worship/non-worship and outward punishment of worship/non-worship, as one must do in order to even argue for enforcing the Sabbath, one has implicitly granted the legitimacy of punishment of outward false worship, thus debunking premise 2. Therefore, those Christians who wish to affirm all 3 premises (a position common since at least the 19th century) have caught themselves in a vicious and inescapable logical self-contradiction.
This is a very interesting thought experiment to me that would result in connecting Baptists to a more catholic, historical, and most importantly, a broadly Magisterially Reformed political theology. John Gill, commenting on Job 31:28 says, "As well as adultery, ( Job 31:11 ) ; by the civil magistrates and judges of the earth, who are God's vicegerents, and therefore it behooves them to take cognizance of such an iniquity, and to punish for it, which affects in so peculiar a manner the honour and worship of the true God", so he evidently thought 1st table offenses could and ought to be punished.
While at the present time, I am not convinced to go against the Baptist 2K theology that I am familiar with in which only 2nd-table offenses are to be punished, I must admit the argument from Job 31:28 is quite powerful. Perhaps I could use the informal/formal distinction of the Old Covenant's establishment (see The Distinctiveness of Baptist Covenant Theology 141) in order to get around it by saying Job is technically under an informal Old Covenant and this law against idolatry is a positive part of it.
Finally, I wish to make clear that the Baptist 2K theology that I represent does not see 1st-table commands as having no moral general equity. It will always be true that idolatry is against the natural law. Our argument is not that idolatry, blasphemy, and heresy are not against the natural law and are not moral transgressions, but rather simply that they should not be criminally punished due to the civil common realm being of a horizontal rather than a vertical nature. The Church will bear the spiritual sword against spiritual sins and the Magistrate bear the material sword against material sins. So, for example, Isaac Backus says, "the nature and end of civil government of any one in the new testament, does it not clearly show that the crimes which fall within the magistrates jurisdiction to punish, are only such as work ill to our neighbour (Rom. 13: 1-10)? While church government respects our behaviour toward God as well as man". Backus sees the sins listed in 8-10 (adultery, murder, theft) as punishable by the government, being 2nd-table offenses that wrong our neighbor, yet, because of the very nature of government under the New Testament era, 1st-table offenses cannot be punished (but this certainly is not because they are moral).
If nothing else, reading Rutherford has given me much to think about. I have realized that things aren't so simple and I can't simply accuse one who wants to prosecute 1st-table crimes of mixing church and state and making the temporal civil realm into the Kingdom of Christ, since an argument can be made to prosecute such crimes by reason of obligation from the natural law and for order in a society that has adopted Christianity as its religion. Ultimately, all nations adopt some national religion. Many of the old Baptist treaties I have read argue simply against persecution, forced conversions, and coerced worship, but Rutherford argues for as much; his positive/negative distinction must be kept in mind in order to accurately represent him. At best, it seems to me that all Baptist typological and biblical-theological arguments prove is that the state is not the church (hardly groundbreaking) and that men should not be coerced to believe. Apart from that, I see no reason why a state should not be able to punish those who publicly go against their official religion. Perhaps I will choose to remain agnostic on the question of religious liberty and not choose between Baptists like those who wrote the 1st London & Gill and those who come after like Backus (though I lean toward the latter, it is not entirely clear to me that it necessarily follows from Baptist Covenant Theology).
But my main positive takeaway here is that, once again, my assessment of general equity in 2nd-table judicial laws has been vindicated, this time by a Westminster divine no less. Rutherford's argumentation, as we have seen, often just assumes that murder and adultery and sodomy demand the death penalty. His attempts to make reductio ad absurdism arguments for punishing idolators depends on this. It is perspicuous to Rutherford as he assumes it is to his readers that such heinous violations against the 2nd table are capital crimes. It is a very strange time that we live in where bestiality is not punished with death, though it is punished harsher than the covenant violation of adultery which receives no punishment though it is doubtlessly worse than a crime with a beast in which no covenant between man and wife is violated, and then at the same time Sodomy not only receives no punishment (yet bestiality does! As does rape even though Sodomy is certainly worse) but is openly celebrated. In short, our penal system is obviously incoherent and violently out of accord with the moral law, which the Reformers rightly understood to require death for such offenses as were required under Moses, given that there is an immutable principle of justice.
Edit: See here, for a good summary of Rutherford's view on the Judicial Laws: https://reformedbooksonline.com/wp-content/uploads/2014/07/samuel-rutherford-on-the-judicial-laws-of-moses.pdf