A recent Ha'aretz article reveals that in 2005, 679 Israeli citizens, most of them immigrants to Israel from the former Soviet Union, applied for refugee status in another country. Of these people, 151 were recognized as refugees and granted "asylum". In most cases, requests for refugee status were made in Canada. The article doesn't reveal on what basis these people filed for refugee status, but from what I've heard in the past, the applicants are usually non-Jews who claim that they faced persecution on religious grounds in Israel. Under the Israeli Law of Return, any "child and a grandchild of a Jew, the spouse of a Jew, the spouse of a child of a Jew and the spouse of a grandchild of a Jew" are eligible to immigrate to Israel.
Many immigrants to Israel from Russia and other former Soviet republics are in fact not Jewish according to religious law. However, this has not prevented them from doing quite well economically compared to past immigrants. In Beer Sheva, a town that has a very large community of immigrants from the former Soviet Union (I'm sure they comprise at least 30 percent of the population), one sometimes gets the impression that every second or third physician is a recent immigrant from Russia, Belarus or the Ukraine. In general, the immigrants from the former Soviet Union, the majority of whom came to Israel in the early 1990s, after the breakup of the USSR, have integrated into Israeli life and all that it entails. You will find immigrants working in all sectors of the economy: from service jobs or security to the high-tech industry. Those who are not Jewish do not face any restrictions on their right to worship, although most are in case secular.
In short, to allege that non-Jewish immigrants from the former Soviet Union face persecution or systematic discrimination in Israel is nonsense. There is certainly resentment and prejudice among "veteran" Israelis against the "Russians", especially in towns in Israel's periphery such as Beer Sheva. It's common to hear Israelis, especially people who immigrated from North Africa or the Middle East in the 1950s and 1960s, complain about the fact that immigrants receive too many benefits and subsidies from the state. People also accuse the immigrants of being mobsters and prostitutes. And, the fact that many immigrants are decidedly secular and have almost no attachment to Judaism gets the more traditional, religious segments of the Israeli population angry. But it seems to me as if it's usually disadvantaged segments of the Israeli population -- poor people -- who express the most prejudiced views about the immigrants. To me, it often boils down to jealousy.
As a Canadian living in Israel, I have to say that I'm ashamed that Canada is granting refugee status to people who are clear frauds, instead of helping people who truly deserve asylum. Those Israelis claiming refugee status are trying to get into Canada for economic reasons. I've always had the impression that there is something very wrong with Canada's refugee policy. Don't get me wrong, I am not against the idea of granting refuge to those who deserve it, whatever their country of origin, but abuse of the refugee system is rampant. I've known quite a few people myself who immigrated to Canada by concocting stories to get refugee status. Even people at Citizenship and Immigration Canada have complained about what is going in their department. The problem seems to be that other channels of legal immigration are too restrictive.