It's passed through the maternal line, racially. If your mother is Jewish, you're Jewish - whether you believe any of the tenets of Judaism or not. Jews decide who qualifies as a Jew, and that qualification is absolutely clear and straightforward. If you can be a Jewish atheist, I don't see why you can't be a Jewish Muslim. Maybe it sounds odd but that doesn't make it impossible. I guess you can also revoke your Jewishness just as you can revoke your citizenship of a country, but if you're a woman your children will still be accepted as Jews, by Jews.
Lebanese protesters storm environment ministry amid trash crisis (AP)
from the article: You can't be a Jewish Muslim