The Erithreans and Sudanese don't get the same benefits as olim. If they get recognized as refugees they get legal status. I think most migrants have no legal status. They still hog on some social services namely healthcare and schools etc.
In recent years there are many migrant workers from the Ukraine, and some other former soviet countries. It's easy for them to get into Israel because there are visa waver treaties with the Ukraine and Russia and maybe some other former USSR countries. But these guys are not pretending to be Jews nor do they get any special benefits.
I don't know how to quanitfy those olim with "specious claims of jewish ancestry". I am sure there are some but my guess is they are not that many. There are many goyim with legit jewish ancestry and the law in Israel allows them to come as olim so they are not fraudsters, if you have a problem with that I think you should advocate changing the laws. My personal opinion is that it should remain as it is.
I don't have a problem with the worker migrast from the Ukraine and eastern Europe in general. They compete for slots that would otherwise go to illegal Palestinians migrants (shabachim). The muslim africans that's a whole different thing.
If they get residency they get all the same benefits as citizens other than voting in national elections but may have to renew it yearly
Only halachic Jews ie those born of a Jewish mother or who had a halachic conversion should get aliyah the law needs to be changed & the rav,ZT"L,HY"d felt that way as well!!!!
A Goy that keeps the 7 Noahide laws can live here as a resident alien but not a citizen
There are 80 % of those from FSU that are not Jews halachically according to the Jewish Agency.
It pisses me off that they are so called "olim" but a bonafide Jew like Chaim can't enter the country.
Chaim,me & others did not fight for Soviet Jewry for Goyim to make "aliyah" but for real Jews to be able to do so!!!
A very small ammount of the Sudanese & Eritreans got legal residency the rest the vast majority are here illegally.
The so called Black "Hebew-Israelite" cult in Dimona from Chicago got legal residency after like about 40 years & a few have been naturalized.