The people who would risk boarding a leaky little boat, being devoured by dragons or falling off the end of the Earth, had to be pretty fucking desperate. They were, not just England but all of Europe was owned/controlled by the landed gentry. If you weren't born into it, or manage to marry into it, you lived by the grace of the gentry. Did the work they wanted you to, ate the food they allowed you to, and worshipped the God they told you to. You had no choice because they owned the land, all the land, plus every plant and animal on it. If you ate any of those plants or animals, you were a criminal. Since jails are costly, you were disposed of by execution, or sold into indentured service in the New World.
But once you get past the dragons, work out your indenture, things look better. Land is pretty much for the taking, England doesn't fuck with you too much, mostly indirectly through the merchants in Boston, New York, Philly. You can find an area where the people speak the same language and share the same God(s). Life isn't exactly easy but at least it's better than Europe if you're poor.
Now these Guys in Philly with their fancy britches, gold watches and book learning, not to mention scary big red headed General Washington, say here we go, one big government to bring us all together. What? Are you kidding? After the boats and dragons, and war, you want us to give it all up? To willingly submit to your will, your taxes, your choice of God(s)? I don't fucking think so. Even most of the people who felt they belonged to the religion which would be chosen as official, didn't think it was a good idea.
The dust up in England around changing the official state religion really didn't mean jack shit to the peasants, they were fucked either way. Whereas here there was more at stake for the little people... and they were armed.
So the wig wearers in Philly heard their plan hooted down, and in order to calm the opposition and reassure the bumpkins out in the sticks, like Rhode Island, they wrote the no state religion guaranty into the Constitution. But that was immediately forgotten until the lawyers figured out how the make a buck off it after WW II. The reality was the communities were far enough apart that if some one with the wrong credentials showed up, the were sent packing. Religious discrimination was open and popular. Several states even wrote laws barring the wrong kind of people from holding public office.
Now, after 200 years of warm and fuzzy, the neighbors are just like us, you want to talk about the founding father's intentions? No, the founding fathers did what they had to do to finish the job, went home and didn't give a rat's ass about what was actually going on in the hinterlands. Look, if Delaware passes and lives happily with a law saying only certain kinds of Christians can hold office. And the Feds don't say anything for all that time, then quibbling over the wording and intentions of the founding fathers is mental masturbation. The feds can force people into the NSA's desert camps, but they can't force people to change their past.