south park: a kosher contradiction

 I've been streaming a bunch of South Park because reasons.

And there's something that has me confused. In "Mr. Hankey, the Christmas Poo" (the show's first Christmas episode), Kyle laments his fate as a lonely Jew on Christmas. At one point, he sings, "instead of eating ham I have to eat kosher latkes.

But one episode earlier, in "Starvin' Marvin" (the show's first Thanksgiving episode), we see Kyle at a buffet with his parents and some other cast members. He is clearly cutting himself a big piece of ham.

This has me so confused...