First, I don't think anyone has snarled at you. You shared an (amusing) story but without a question to guide conversation, so naturally people are responding to what jumped out at them.
I agree that it's pretty funny that you two were a bad match on nearly every conversation topic.
I also, like many posters, thought it was a bit of an overshare. Not in the sense of "can you believe this woman told me all this TMI about herself," because even though i do think sharing information about your exhusband being a deadbeat dad and that sort of thing is waaaay too much for a first conversation with a stranger, obviously he was interested in sharing the same level of detail about his life, so it was no problem. Instead, as others have said, it's disconcerting because you've given a lot of information that could be used to hurt you. I'm not the type of person to suggest that women spend all day locked in their homes holding a can of mace and reading the Gift of Fear, but I do think giving certain types of information too freely can open you up to being a victim if you tell the wrong person.
Also, I do think you were rude for suggesting he visit a local nondenom church. I think in the context of the conversation you were having, it would have been fine for you to respond to his statement by asking more about why he doesn't like organized religion or explaining why you like your own religion or bean dipping, but I don't think the proper response to "I don't like organized religion" is ever a suggestion that someone go to church. I think the above analogies don't totally capture the situation because religion is so much more personal/private/intrusive than meatloaf or ultimate frisbee.
There are a number of reasons a person might say they don't believe in organized religion. For example:
1) they grew up in a Christian church and are still Christian but didn't like all the rules/strict structures
2) they grew up in a Jewish/Muslim/Hindu household and still hold some or all of the beliefs but don't like to attend (place of worship) and do (rituals of the religion) etc
3) regardless of how they grew up, they find the history of religious institutions (eg crusades) to be off putting and don't want to belong to one
4) they are interested in the idea of a God/higher being but don't think humans have found the answers and don't want to be part of a structured religion
And on and on and on. And of the wide range of reasons that someone could "not believe in organized religion," your suggestion could only be useful for someone in category 1, in my opinion.
TL;DR: In general, suggesting that someone go to a Christian church when they tell you "I don't like organized religion" is both a rude response and not a particularly helpful one even if they're open to solutions to their dislike of religion unless you know they have Christian beliefs.