He wasn't Jewish if he didn't believe in Judaism

Jewish is an ethnicity. Ethnicity is something you choose. You can change your ethnicity unlike race. Hebrew comes from Abraham, Israel comes from Abraham's grandson Jacob, and Jew comes from Jacob's son Judah. Jew isn't inherently a religion anymore than Hebrew or Israeli are religions.

"The Jewish people has no fatherland of its own, though many motherlands; no center of focus or gravity, no government of its own, no official representation. They home everywhere, but are nowhere at home... You may prove yourselves patriots ever so true, you will still be reminded at every opportunity of your Semitic descent. This fateful memento mori will not prevent you, however, from enjoying the hospitality extended, until some fine morning you are cast out of the country, until the skeptical mob reminds you that you are, after all, nothing but nomads and parasites, protected by no law... We must prove that the misfortunes of the Jews are due, above all, to their lack of desire for national independence; and that this desire must be awakened and maintained in time if they do not wish to be subjected forever to a disgraceful existence." - Leo Pinsker, 1882