There are certain shared qualities between the black and Jewish communities which may be why so many Jews feel connected to the black community and to the BLM movement. The Jews were at the forefront of the civil rights movement
I would like to point out two of these shared qualities.
1] There has always been and will always be anti-semitism. No matter what. When we are socialist we are hated for not being capitalist. When we are capitalist we are hated for not being socialist. When we are rich we are hated for not being poor. When we are poor we are hated for not being rich. When we are religious we are hated. When we assimilate we are ALSO hated. The Holocaust happened when there was mass assimilation in European society. We are hated for being moral and hated for being immoral. No matter what we do and how hard we try to please there are always people who hate us. Just say the word Jew and evince hatred from people who have never actually met a Jew!
Blacks are also the subject of hatred. There is nothing anybody can do to change this unfortunate fact. People, white and black, can torch businesses, vandalize buildings and loot department stores in protest - it doesn't matter. People will always hate people for the color of their skin [until Moshiach comes]. Congress can legislate in favor of blacks but they can't legislate to force people to change preconceived notions against blacks.
2] The hatred of Jews is not only because of exogenous factors. For example, we have a reputation of being less than honest. This is well earned. Someone told me that he was driving through a well known Orthodox neighborhood and pointing out house after house where the tenant had been involved in and caught for financial wrongdoing. Irreligious Jews also steal and commit fraud and find their very Jewish names and faces all over the newspapers. We hear people saying "I did shtick" or "he did shtick" which can mean juggling in front of the chosson and kallah but also is an elegant way of saying to steal or defraud. Plenty of non-Jews steal also but maybe because we are so smart, we do it in a big way. See entry "Bernie Madoff" as one of countless examples.
This is of course deplorable. גזל עכו"ם is forbidden and includes even the worst type of Goy. One may not steal. Period. But we do. I personally have had so many negative experiences with Jews and money, that I have come to the point where I trust just about nobody. Jews don't discriminate and steal from Jews and non-Jews alike. Our bad reputation in this area is well deserved. The GEMARA already tells us רובן בגזל - Most Jews in some way are dishonest in monetary matters. So instead of always blaming our bad rep on Anti-semitism we can work to improve ourselves in areas where we find ourselves lacking, such as ישרות.
Black people also have a bad reputation for certain things which is well earned. One example is their disproportionately high crime rate. Quick - Name a dangerous neighborhood that is predominately white? You can't? Either can I. Now name a dangerous neighborhood that is black? It didn't take you long nor did it take me.
Another well known problem is the habit of siring children with women who are then abandoned with no means of support only to go on to the next one and do the same thing. This is one of the biggest problems in the black community and is not the fault of white people. Nobody stands with a gun pointed to the head of a black man and forces him to have relations with an unprotected woman and then leave her with no trace of his whereabouts.
The conclusion is that there is a limit to how much we can excise and expunge anti-semitism and racism from our midst. The other conclusion is that we should all take responsibility for our failings, both personal and communal. If we do that, we will make the world a MUCH better place.