Freedom of religion was supposed to be a thing in the US. Sin is not a good reason to make a law that binds those who don't follow the same religion

The first amendment restricts congress, not voters. Voters are free to vote for whatever politician they like for whatever reason they like, including religious reasons. The constitution does not demand that religious citizens demarcate and compartmentalize their religious and civic beliefs when they go to vote.

In theory it should restrict the representatives who got voted in from using their religious beliefs in legislating

It doesn't even do that. It restricts what kind of laws congress can create, not the reasoning congressmen use when choosing which laws to support.

Completely secular and constitutional laws may be enacted by congressmen that have religious reasons to support that law; e.g. religious legislator may vote for a law against murder because murder is against their religion. The first amendment doesn't regulate the thoughts and reasoning of legislators; religious reasoning for secular laws are fine.

And conversely, secular reasoning for religious laws doesn't make the law okay; a cynical atheist might say that religion is necessary for controlling the unwashed masses, but despite that secular reasoning, a law mandating a religion would still plainly violate the first amendment.

We fought a whole war to end chattel slavery because a movement largely composed of pious Christians believed it to be sinful.

There was also a large amount of Christians who thought slavery was permitted by the Bible so I don't think that argument has a leg to stand on

What argument? The point is that everybody votes based on their particular opinions of what is moral or immoral, often related to their religious beliefs, this is not a new phenomenon, and it is not at odds with freedom of religion.

The point is not that all religious reasoning leads to constitutional laws; that is obviously false. The point is that religious reasoning dos not necessarily lead to unconstitutional laws.