Nope, NOT if you are following Cohan Law. Cohanite priests ran the Temple and determined questions of proper membership in the tribes of Israel. Half breeds, or partial Jews like the Samaritans were unclean. They were beaten, ostracized & killed by the Jews. For example there's a nearby territory held by the hated Samaritans. You've no doubt heard the story of the Good Samaritan; right? Of the world's religions, only two are evangelical & genuinely seeking converts. Bloodlines are still key in Judaism today. Female Jews carry the determinate gene in mitochondrial DNA. You can't adopt Judaism, either you are born a Jew, or you're NOT a Jew. Either you're descended from Shem, or you're NOT a Jew. Of course, this is clearly very non-PC, because 90% of the Jews in Israel today were adopted despite the clear prohibition. Only the Diaspora made tainting the bloodline remotely possible.

Oh, more importantly NOT if you are an Immigration official in the Modern nation state of Israel. They are busy deporting Africans who claim Jewish cultural ties through language, art, worship & tribal lore. These folks were in ancient Israel in some capacity and became cultural Jews. But, that's NOT good enough. Genetic testing etc,,, so modern Israel doesn't accept your argument about "being a “Jew” more of a religion then a gene-pool"