There are at least some of us religous people (I am Christian) who agree that religion shouldn't run government.
Personally I think my church and every other church in the USA should pay taxes. Jesus was not anti-tax! (heck, he told people to pay their taxes) I also think ministers shouldn't have special rights to marry people - either let everyone who meets some basic requirements be able to be an officiant or let nobody but civil servants. But don't give religion a special place here. If I want my minister to marry me, let that be simply a 100% religious event, with no civil significance - and likewise let my civil ceremony have no religious significance if you so desire.
The Puritans (at least a significant group of them) had it right concerning marrigage: they established marriage as an entirely civil matter initially in the northeast USA. They didn't see marriage as a rite specifically discussed as a in the Bible (they saw the Bible talk about marriage, but not commandments about the order of the actual ceremony nor anything that indicated it was a duty of an overseer, bishop, elder, etc), so they kept weddings out of their churches. If you wanted to get married, you went to the courthouse and didn't pollute the church with your civil contract. The minister most certainly didn't marry you! (some also did "bundling" if they wanted to make sure the guy didn't try denying he impregnated the gal - the parents let them sleep together in the daughter's room prior to marriage, so that he couldn't deny the kid was his, putting the gal in the unfortunate position of no longer being seen as an attractive [and valuable financially] mate to anyone)
The Baptists and others in the south had different ideas - that's where the US idea of a church wedding came from, outside of some denominations that view marriage as a religious event (such as the Catholic church).
The idea of the church legislating marriage isn't universal.
And personally I'd just assume to keep politics out of my church period. I think there are few things less holy, honorable, and good then politics, so I'd rather keep them as far away from the holy, honorable, and good as possible.

It does go both ways. When the church starts politicking, it gets corrupted. I'm not the only one that sees it this way, although sadly a lot of US Christians have been basically brainwashed into thinking that God, being all-knowing, would want one of our candidates to win an election! What a small god they serve.

That said, some churches will continue to think that somehow God would be pleased if they made the stupid laws rather than letting elected representatives do so. And I don't think anyone will stop that (and this is hardly unique to Christianity - it happens in all major religious as far as I can tell). All we can do is speak out against it and make sure to vote for candidates who understand the difference between church and state. I'm probably a "bad" Christian to some (I try to think!), but so be it!