Boy, we sure do love to write about comic book characters. The problem is, every time we think we've got their backstories nailed down, the universe changes and all of that history goes into the wash.
Hal Jordan, Green Lantern (not to be confused with Alan Scott, Guy Gardner, Kyle Rayner, and John Stewart, also Green Lanterns), is the perfect example of continuity gone wrong. We're not talking about crazy plotlines, that's to be expected. We mean whole swaths of history being written, then written out, then put back in randomly, so that it's impossible to tell what is canon and what isn't.
In the 1960s, Hal was a test pilot (a la Chuck Yeager) and a daredevil. Then in the 80s he was a recovering alcoholic with daddy issues. Then in the 90s he was... dead. Then he was the undead spirit of vengeance. Then he was alive again. He had brown hair, then grey hair, then brown again. He was in a serious relationship with his boss. He was in a serious relationship with a young alien who had artificially aged herself to avoid accusations of statutory rape. And so forth.
How much of this history is canon in the current universe? Ummmm, some? Honestly, we're not entirely sure and it's pretty clear that GL's writers aren't either. Or if they are, well, that may yet change.
So yes, in a comic from November 2015, Hal announced that his mother was Jewish, making Hal, himself, a Jew. Hooray!
In January 2016, DC rebooted their entire universe (again). Did Hal's Judaism survive the cataclysm? We have no idea. More importantly, we honestly don't care.