You wouldn’t ASK them to desecrate shabbat, obviously, and you wouldn’t feed them treif food, and such a woman’s offspring would be halakhic Jews (Although they wouldn’t be very Jew-ISH), but as far as giving these people any of the zechuyot that come along with being a Jew, they’re not entitled.
Someone like the OP, sadly, should be treated like a goy le kol davar. I wouldn’t allow him to cook my food, or count him towards a minyan, or allow him to touch wine. His case is not that of the child who never had shabbos in his life. A person who casts off the yoke of torah and mitzvot is a very tormented, troubled soul, in my opinion.