The secular government of Israel allows many non-Jews to immigrate. Such immigrants either take part in a recognized non-Jewish community, convert to Judaism, or travel outside of Israel if they want to do something like get married.
Two converts to Judaism could marry and have many children who would be 100% Jewish without having any Jewish DNA at all. And the paternal half of one’s DNA could be ‘Jewish’ without one being a Jew at all. The confusion over this is why American Jews are in danger of writing themselves out of Jewish history like Sadducees, Samaritans, Sabbateans, Frankists and others.
Exactly. I doubt Sammy Davis Jr. had "Jewish DNA", which is irrelevant.