Anyone can become Jewish. But are these Nigerian "Jews" really descendants of Jews? They may want to live like Jews and that's fine. Other "lost tribes" have more of a claim than they do. (rant warning)
I believe that all the other "nations" that are suddenly accepted as Jews (Ethiopian Jews, Kaifeng, Bnai Menashe etc..etc..) had some obvious Jewish ancestry in the past. But they are not Jews, just Gentiles from "lost nations" of Jews who are now dead. Obviously their Jewish ancestors intermarried so much and carelessly did NOT build mikva'ot or battei din in their communities- so their intermarriages may not have been valid conversions- or never bothered to convert...so all their descendants today are Gentiles. Their ancestors did not even keep records of who was a Jew and who was not. I am not trying to be racist, this applies to all the "lost Jewish nations" of any race. Those who are Jews have the paperwork to prove it. Those who do not, are not.
It really baffles me. If Moshe and Chava go to a Beis Din to get married, what is the first thing the Beis Din going to ask them to show? Parent's ketubot. Grandparent's ketubot. Any proof of valid Halachic conversions, proof of any get...sometimes even proof of parents or grandparent's burial in Jewish cemeteries.
Without PROOF, Moshe and Chava would NOT be allowed to get married. And without proof, Moshe and Chava would be declared not Jewish and would have to convert. Depending on their situation, it could be a quick "just in case" conversion or a long one or two year process. I have seen cases where a young man and woman want to marry but one had a mother or maternal grandmother who did a "conservative conversion". Or other cases where one came from a former USSR country and lost all documents and had hired investigators to go to Beis Din and show the judges the proof. It's not a simple process.
But if you are a "Jew" from Africa, India, the Amazon, China etc... and you have NO proof of Jewishness....it's ok. It doesn't matter, you're just a lost Jew who deserves to make Aliyah and can be recognized as completely Jewish. I must be missing something. Sfardic Jews, Mizrachi Jews, Ashkenazic Jews etc are Jews today, because when their ancestors were establishing their communities, they were very protective of their Jewishness and made sure they were careful to keep records and religious courts. But all others whose ancestors were careless in this regard, never bothered to build courts etc... they can be declared Jewish at any time. No problem, especially if they are not white, then of course they can be declared "lost Jews". How many more people will now declare themselves to be "lost Jews". There really needs to be some definitive ruling on this. Any Gentile can want to become Jewish, that does not mean they are or should be...unless they can live up to the 613 laws. And now whole groups of people are desperate and want to be Jewish out of their own desperate delusion that they are now declaring themselves lost tribes. And it has to stop. Convert to Judaism if you can live up to it. Otherwise, stay a Gentile. Your ancestors did not provide you with a Jewish identity for a reason, so either accept it and convert or stay a Gentile but please stop trying to force yourselves into Judaism as a "lost tribe".
As far as these Black people. If they sincerely converted then they are welcomed as Jews. Obviously. And let's not forget that there are plenty of black Jews who have black Gentile fathers and white Jewish mothers, so yes there are black Jews from birth too.
My only concern is that Israel is a small country....honestly, how many people can it absorb? (And as far as Israel loosing immigrants, Jews from first world nations would be more freely able to leave Israel but these people from third world countries have nothing to go back to, so they will stay). And second, the greatest concern is- how many of these people convert to Judaism out of a deep desire to be a light unto all nations and serve Hashem and accept the Yoke of the Torah? And how many may have ulterior motives? In other words, are they all sincere converts? Or are they converting just so that they can get a better life? I thought that to be able to immigrate after a conversion, people have to live one year in a Jewish community and show their sincerity. Hopefully these couple thousand people who are arriving to Israel as Jews are complete and total SINCERE converts who want to add to the Jewish nation in the goal of blessing the world and not have any ulterior motives. (May they add to a religious community and not end up going back to their former ways or having their kids think they're Jews but running around Israel half-naked at parties on Friday nights) Not like the new Ethiopian Miss Israel and others- who don't care about Judaism.
Those who are arriving to Israel and did an insincere conversion for the purpose of a better life only- may end up (or their descendants) becoming a curse to the Jewish people.
In the end, them arriving to Israel is what Hashem has allowed to happen. Hopefully it is for the best.
Rant over