Supposedly Pilate pissed off the Jewish population repeatedly in his governorship by pushing Roman religion and minting coins with non-Jewish imagery, so I think we can safely say he wasn't Jewish and was presumably Greco-Roman or Mithraic.

https://coinsite.com/the-pontius-pilate-coinage/

Not being a literal expert on the topic I'm not sure whether the imagery used implies one but not the other.

Definitely not Jewish though!