Being Jewish is not a requirement for being a citizen of Israel. It may be a requirement for immigration to Israel, on that I am not certain. But Palestinians and other Non-Jewish Semites, who are born in Israel of Israeli citizens, or were in Israel when Israel was formed, are indeed citizens of Israel and can vote in Israeli elections.
One reason we should support Israel is that it is a democracy that grants rights to it's citizens, not granted by the Arabic and Non Jewish semetic states which surround Israel.
According to Israeli law, a Jewish immigrant has a right to Israeli citizenship, but other immigrants are on a case by case basis. Understand this is for the secular Israeli definition of Jewish which is a good deal more permissive than the religion. This was originally so that WWII era refugees didn't have to prove their religious status (Hitler didn't care either).
Thus also the recent controversy about some of the post-Soviet Russian immigrants.
This "right of return" doesn't mean that the Israeli authorities systematically put up with a lot of nonsense. They have been known to extradite Jewish criminals to the United States with the understanding that they could come back to Israel to live after serving their time in the USA.