Well, it would to the Israeli state and to a Nazi. Because in both cases it's a "blood" question--not a religious question and not a cultural question. If Bill showed up with a birth certificate that designated his mother's religion as Jewish, he would be Jewish; he would enjoy the right to live in Israel or the right to march into a gas chamber--depending on who was running the shown. I believe the right to return is currently granted to a Russian whose grandmother was "jewish" -- I'm not sure what the evidence required would be. But it seems to be good enough for a state that seeks to expand its population.
For my own part ethnic identity doesn't mean much and I have come to understand that all forms of identification are ultimately a form of mental lazyness. But hey, History is not so wise and one would be foolish to ignore it.
Joanna