I was recently in Israel, and talked with an jewish man, with an ethiopian background, about the Law Of Return that allows everybody with a proven jewish background to live in Israel and become Israeli citizens. He talked about the problems with ethiopian jews, and that they where invited in the 1980's and early 1990's, but had experienced many problems with being integrated into isreali society. I have had problems finding quality information on this problem, maybe somebody here can help me get a better understanding of this issue?
I can talk about some of the initial difficulties, at least from the religious angle.
Over the course of the 20th century, the Falashas or Beta Israel (House of Israel) of rural Ethiopia who practiced a Judaic, Hebrew Bible (Old Testament)-based religion and saw themselves as Israelites came to understand themselves as Jewish. In 1973, Israel's Sephardi Chief Rabbi, Ovadiah Yosef, ruled the Beta Israel officially Jews, "descendants of Jewish tribes who moved south to Cush...they originate from the Tribe of Dan on the basis of the most reliable testimony and evidence." The Israeli Ministry of the Interior adopted this ruling into law, giving the people of Israel the right of return (automatic entry to Israel and citizenship).
Although there were pockets of immigration earlier, between 1984 and 1991 the vast majority of the Ethiopian Jews migrated to Israel, most famously in a series of airlifts from Sudanese refugee camps (Operation Moses, Operation Solomon).
Once in Israel, they faced numerous challenges. There is of course the obvious, ongoing trauma of migration. Many parents lost children before and during the airlifts; many children lost parents. The Beta Israel had been rural and isolated in Ethiopia; they suddenly found themselves having to deal with life in modern urban centers. I've not read anything about whether/what kinds of racism they had to deal with as marked outsiders (but that just means I'm really a medievalist who dabbles, often incompletely, in African history).
But it wasn't easy from a religious angle, either.
First, there was the question of Jewishness. Despite the official ruling, Israel's religious authorities questioned the status of Ethiopian Jews especially when it came to questions of marriage and divorce legitimacy. A key point of tension was their requirement that Ethiopian immigrants undergo the ritual conversion process. Obviously this did not sit well with the Beta Israel, who were perfectly clear that they were Jewish--why convert? The ritual mikveh bath reminded a lot of people of the sporadic forced baptisms they had had to combat in Christian Ethiopia.
Second, religious/community authority. Back in Ethiopia, it had greatly benefited Beta Israel to be so isolated and self-governing, given the periods of religious hostility and difference in general. The qesoch, Ethiopian rabbis, exercised enormous emotional, spiritual, political power. In Israel, they were suddenly denied, among other things, the ability to confirm marriages. Beta Israel perceived this as a great threat to their authority and even their spiritual powers as guides in general (as well as a strike against their Jewishness as a community).
Third, there was a pretty fundamental difference in religious viewpoint between the Beta Israel and the rest of the Israeli community. The Ethiopian Jews had based their religious beliefs and practices on the Hebrew Bible--they had no Talmudic tradition, no access to the wealth of commentary and laws and scholarship that has built up quite a lot of modern Judaism. So there were some theological/ritual clashes, too.
Fourth, the shift from rural to urban created religious problems for the Beta Israel, in addition to the general culture shock we might expect. For example, women's experiences during childbirth. In Ethiopia, childbirth needed to be a protected, separated experience to guard the mother's modesty and protect everyone's purity. Women in labor secluded themselves in either their family home or a ritually designated Ya Dam Bet, remained clothed throughout the process, crouched down, and were attended by only the closest relatives. After the child's birth, they and the new baby remained secluded for either 40 or 80 days. The idea is that this gives the community time to accept the infant as a member, and frees the mother from demands placed on her by daily life (or, you know, everyone needing to hold the baby...). Even circumcision in Ethiopian Jewish communities is a private event--which caused problems initially, when well-intentioned workers helping new arrivals in 84-85 tried to hold the circumcision ceremonies in a synagogue.
In Israel, suddenly new mothers had to give birth in hospitals, with strangers present, dressed in hospital gowns, on their backs where "you see everything, even how the baby comes out." And the seclusion period after the child's birth, which was seen as vital to protect community purity and restore the mother's? Ethiopian Jews found it very hard to manage nearly 3 months of social isolation in a thriving, secularizing city. Minuchin-Itzigsohn et al. describe some of the ways women tried to deal with the traumatic shift: creating corners of isolation for themselves within their homes, having their husbands move out for the duration of the seclusion period, not cooking for their families, not having sex.
Unfortunately, I'm not familiar with the second half of the story (most of which might be a question for /r/AskSocialScience? or if there is an Israel sub?). But this is some of the historical background on the challenges.
Since integration is an ongoing process, Most of the answer to this question is past the 20 year rule. But we'd love to answer it over at r/israel !