Dear Neville,
“How people self-identify is completely meaningless.”
Exactly! If a yid identifies as an athiest or nilhist it doesn’t change his status until he is actually meeting certain criteria.
“Would you eat the food of a polytheist … and still acts Jewish?”
So how is he a polytheist? If he serves as such, than he is a mumar l’avodah zara and is not believed on his food. If he is a mumar for just praxis his food may also be problematic. If a Yid is certifying the food, than e can eat it. How does this prove anything?
Leaving Judaism is a problem of a mumar l’chol HaTorah as I explained in the other post. Even if he believes and worships correctly.
“…then everyone is still considered fine.”
No. It is not fine at all. But we are still included in the mainstream enough that there is no benefit to calling out theological differences.