Unfortunately, not even Israel is immune to having bigots. No nation is.
I think a lot of the issues come from how the Ethiopian Jews came to Israel, at least en masse. There was a huge airlift that brought an entire population into Israel and at that time really taxed their society. Many of these Jews were rural and had no access to electricity. Israel had to educate an incredibly huge population relative to their size, transitioning from sheep herders to people who can work in modern metropolises. For many older Israelis, this image of Ethiopian Jews remains, which probably explains why all the problems seem to come from the older generations. I don't think I've heard of an issue from the younger Israelis, many of whom never saw this and served in the army with them. Ethiopian Jews themselves do report on how equalizing the army can be, and we do know that increased contact with populations tends to reduce bigotry.
There could be other factors, such as conflating Ethiopian Jews with illegal immigrants from other African nations. Israelis do differentiate between the two, but they can't always know and that can lead to some incidents. Also, some people can just be racist.
In general, Israelis aren't as racist as most people make them out to be. Ethiopian Israelis still love their nation very much, as well as the people who live there. At least, I know some Ethiopian Israelis myself and they're very proud Israelis and have never reported extreme discrimination.