I considered Peter being Catholic too, because like you said, his relatives seem to be Irish. I think that would sense make too.
But in my opinion, if Peter was a Catholic it would've been made more explicit by now. Sure, it wasn't until the 2000s (I think?) that Ben Grimm was declared 100%-no-denying-it Jewish, but other Marvel Catholic heroes (Kurt, Matt, Eddie if you consider him a hero) have explicitly identified themselves as Catholic at one point or another. Peter hasn't. Hence why I think he's probably Protestant. Or "unindentified denomination that isn't Catholic".
As for Peter being Jewish.... yeahh, it wouldn't really work unless his mother was Jewish. You're right. (If I had a nickel for everytime I had to explain to people why my father having Jewish doesn't make me a Jew... oy.)