What does it take for a group to not be considered halachically Jewish anymore

Let’s say “totally hypothetically” you have a certain Jewish cult group that justifies and celebrates terror attacks against Jews while calling for even more violence against Jewish people and allying themselves with people who call for a second Holocaust (while denying the first).

Are they still halachically Jewish? Do you have to treat them like a Jewish person halachically, for example not hating or speaking ill of them? Can you drink their wine and trust their shechita? Count them in a minyan?

If a group literally supports a second Holocaust (“hypothetically”) are they still considered halachically Jewish?