1.) Most of the US Founders were Deists, not Christians. While they believed that there was some Deity or Cosmic Force out there, they did not believe that the Bible was an accurate depiction of that being, or even a good record of ancient history. Jefferson specifically referred to it as “the word of a demon”.
2.) That being said, a small number of them were Christians who believed in the idea that individual states had the right to form theocracies. The early presidents, Madison in particular, said “LOL nope” and did what they could to punish the states which tried.
3.) The First Amendment should be enough to put that idea to rest; but sadly there are a lot of alternate (and dubious) interpretations based on a “plain reading” of the text in a vacuum. The fact that it’s fairly easy to find writings by the Founders about what they really meant when they were creating the Constitution and the Bill of Rights apparently doesn’t matter.
Now, posting or teaching the 10 Commandments isn’t, in itself, unconstitutional, as doing so as an individual is a form of protected speech. But it’s been ruled, again and again and again, that the US government cannot be seen as endorsing *any* religion, and public schools are government-funded and under purview of the Department of Education. It’s not even like Christianity is particularly targeted here, it’s just the religion which comes up most often due to being the majority religion. (It’s also not a case of “the rich and poor alike are forbidden to sleep under bridges” because Christians are the majority and don’t suffer any special or undue hardship compared to anyone else because of it.) Trying to do an end run around the spirit of the law with things like “The government isn’t doing it, *I* am doing it on behalf of the government” or “…But muh made-up version of history!” has never worked in the past, though with the current Supreme Court who knows if that will last.