You don't? I guess that's a big difference between liberals (like me, and I don't think it's a bad word) and conservatives maybe? I think it would be awful to split up the country because of our differences. Our differences make us better.
The Establishment Principle requires the magistrate to protect Christ's Church and apply the Ten Commandments in making the civil laws of a land, while Theonomy is one way of making those civil laws. So it is possible to have the Establishment Principle without Theonomy. And actually, it might be possible to have Theonomy without the magistrate protecting one Church denomination, though I would need to think some more about that.
Theonomy arose out of the neo-Calvinist concept of sphere sovereignty whereas Presbyterian establishmentarianism (a qualification which must be made in view of the fact that there are Erastian establishments) is grounded on a two kingdom foundation. In the former there is no secular-sacred or nature-grace distinction. In the latter these distinctions are fundamental.
I am increasingly coming to the conclusion that Capital Punishment should never be used. I had been uncomfortable about its use since at least 2012 and since then my position is that it should be used sparingly if ever. Most people being sentenced to death are probably going to Hell. Killing them removes the ability for them to repent. Even if they do not repent, I don't think that Christians should act as agents of God's judgement.
I'm not sure why you've changed your position so quickly? Have you heard of the ex-gay movement? I pray for the homosexuals that they would change, and change is possible. Norma McCorvey is both a former pro-abortion advocate and a former lesbian, and she was able to change.
Also, what happens to Jews, Muslims, etc. in Theonomy?