Being Jewish is odd at times. For instance, one can be a BuJew (Buddhist-Jew), but a Jew for Jesus is out. Once there were Muslim Jews, but they were anomalous and eventually absorbed by Islam. The first Christians were all Jews, but then there was the decisive split and they went their separate ways.
But can one be a Muslim Christian, or a Hindu Muslim? I think as far as Abrahamic faiths go, at least, you can’t be two things at once. How about a Jewish-Christian-Muslim? “Y’know, I think they all had it right!” What a felicitous thought.
One factor that appears unique to Jewishness is the Jews-as-a-people/ Jews-as-a-faith paradigm. This is confusing not least of all to Jews. I don’t believe in YHWH, God, or supernatural authority in any guise, yet I am still Jewish. I find no contradiction there, though perhaps if all Jews were atheists Jews would eventually disappear. But one cannot force oneself to believe what one doesn’t believe simply because it may be a “historically conscious” choice. What to do?
Each must in the end follow his or her own conscience. The memes will take care of the rest.