I think it helps to know the religious climate in which the Founders were operating in.
Even in the last years before the American Revolution, there were still people arriving with the promise of religious freedom - only for many of them to face the same kind of oppression they faced back home, depending on where they ended up. After the Revolution, some of the States became theocracies, or tried to - in particular, the Anglicans in Virginia which had largely taken over the state government tried to make Virginia an Anglican theocracy, only to end up with the strongest guarantee of religious freedom [at least on paper] thanks largely to the efforts of James Madison. A few of the Founders were happy with this state of affairs and pushed to allow states to establish an official religion or even a theocracy, but aside from Patrick Henry, barely anyone other than historians know their names (and most Americans who remember their history lessons only know Henry’s name because of the Revolutionary War, not anything he did after). For the rest, it offended their sense of freedom and justice, and some of them feared the day when the kind of sectarian violence which had plagued Europe for centuries would arrive.
So the 1st Amendment was written specifically with that in mind. And they repeatedly affirmed that yes, this was totally what they meant; while most of the quotes about religious freedom we still use today were written by Jefferson or Madison, they weren’t the only ones who went out of their way to establish that. Actually stamping out the de facto theocracies which had sprung up and refused to relinquish power took a few decades, because the early US Government was underfunded and had limited enforcement powers… but it was a major priority for a lot of them, so they did what they could. There have been occasional court challenges to the idea that States can’t establish official religions, with the last serious effort being in 1961, but it never goes well.
Some people might say “but they still only would have cared about Christianity, right?” Nope. Aside from the fact that most were (or later became) Deists and Deists don’t necessarily consider themselves Christians, they very much intended to protect “Jews, Musselmen [Muslims], and Turks” as well. Admittedly I don’t know how many of them would have had Atheists and/or Pagans in mind, but still.
TL;DR a bit of early US History, for context.
