Correct, because they wanted to leave it up to the state and created the 1st amnd. to make sure it was.
this is incorrect. there were 2 branches of the founding fathers, ones that wanted just federal law, and ones that wanted just state law. in the end they made a compromise, that states could have their own laws, but be subject to federal law which supersedes it. so states can make laws as long as they do not violate federal law, so anything beyond having a state law to declare an official religious sect as their mascot would never have stood up to scrutiny. not in the time of the founding fathers or today.
just the statement of "they wanted to leave it up to the state" isn't correct. half of the founding fathers didnt want states to have almost any power at all.