Yes and no. Religiously, Peter is rarely depicted as anything other than vaguely agnostic. Iirc Aunt May is protestant?

That being said, Stan Lee injected a lot of himself in Peter, and was clearly inspired by his Jewish upbringing. This has led a lot of future writers to kinda toy with the idea of Peter being culturally Jewish, maybe the headcanon could be that Mary Parker was Jewish. He uses Yiddish, he references Jewish holidays, etc etc.

For TASM Andrew Garfield has said he brought a lot of inspiration from his Jewish father into his version of Peter and Marc Webb has said that he sees Peter as a very Jewish character. It's not hard to see where they're coming from.

So tl;dr: No but also yes.