Not really, he's never been. This Peter Parker and pretty much every single iteration of Peter Parker have always been a Protestant Christian. The few times he's shown in a place of worship, he's in a church and never in a synagogue.

I think the only Peter Parker who might have been Jewish was Peter B. Parker from the Spiderverse movie and that was due to showing him stepping on a glass during his wedding, which is a Jewish tradition, but that could also mean that his universe's MJ is Jewish. However, Peter B. is an OC from Spiderverse and isn't the "main" Peter Parker which most stories are based on.
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I always thought that it was because he was trying to impress or show off in front of the landlord's daughter since Mr. Ditkovich is kind of a stereotype of Slavic Jewish people.