Berklee students sing Hallelujah

That doesn't make those composers any less Jewish. Now in many cases, they were doing it for money - there's just a lot more to be made catering to Christmas than, oh, Rosh Hashanah. In Cohen's case, he was expressing his quest for inner truth, but he always came back to his birth religion:

Of course, Cohen was catholic in his religious influences. His songs are replete with Christian as well as Jewish imagery, from the bleeding cross to the Sisters of Mercy to “my sacred heart.” And everybody knows that he was a restless seeker after spiritual truth, spending many years as a monk in the Buddhist retreat on Mount Baldy, California.

But he was always at pains to stress that none of this meant he ever broke from Judaism. He told the BBC in 2007 that his “investigations into other spiritual systems have certainly illuminated and enriched my understanding of my own tradition,” but that “I very much feel part of that tradition - and I practice that and my children practice that. So that was never in question.”

"Hallalujah" itself begins:

Now, I've heard there was a secret chord
That David played, and it pleased the Lord

Kind of Old Testamenty right there. To turn that particular song into a paen to Jesus?