Many Jewish groups objected to the Seinfeld show precisely because he WASN’T openly Jewish. His character never identified himself as Jewish, none of the girls he dated ever were identifiably Jewish, and there were no signs of jewishness around his home.
Just a slight exaggeration. I can’t remember if his character ever identified himself as Jewish, but there was at least one girl he went out with who kept kosher. And after Elaine was told by a rabbi that she has “shiksappeal” she asked Jerry if that were true.