I definitely feel that it is important to pass on the cultural part of Judaism, if not the religious part. I meant it when I said that there are a lot of Jewish atheists - there are even secular humanist synagogues. But he seems to be rejecting it all, and even more than that, he can't seem to be tolerant of any ritual observance.
Again, have you or your husband asked him why it bothers him? I'd give him lots of time to answer. Then ask what he likes about his religious school. But don't frame the question as "If you hate religion here so much, why do you like school??" Try asking gently what he LIKES and leave it at that.
I'm going to ask a question, and I hope I'll sound gentle.
Okay. How long is the Shabbat ritual on Fridays? I attended one once, and it lasted for 20 minutes or more. I remember ritual handwashing (each person), blessing the candles, and a blessing with bread, and maybe more? There were some long prayers. Not sure. Either way, it was long.
If this is the ritual you follow, I can understand why a hungry, growing, nonbelieving teenaged boy might react negatively to doing this every Friday. I do like the idea of asking him to help you cook the meal. That's fair!
I can understand that rejection is difficult for you. Maybe you need to explore why he's so hostile. Religious school and religious observance at home sounds like a lot, IMO. I know there are Jewish atheists, but I'm not sure if that's the point here. I'm still wondering about rituals being a trigger. Your son would know. But also IMO, the conversation would have to go carefully to avoid flaring tempers.