I've heard that many Communist regimes descriminated against certain groups despite wanting equality and that Mark himself was an anti-semite. Is this true?
No and Sort of....Marx's father was a Jewish lawyer who converted to Christianity in 1817 due to the Anti-Semitic laws in Prussia that would have otherwise bared him from practice. Sartre's "Anti-Semitism and the Jew" discusses some of Marx's analysis of Anti-Semitism (he explained the material basis of Anti-Semitism, which he predicted would fade away under communism). It seems like your question about Socialism is about the USSR, so I will answer the second half of your question about the USSR. You see, before the 1917 Revolution, between 1880-1917 there was wide spread Anti-Semitism in the Pale of Settlement (where Jews primarily lived). The government would have pogroms regularly where ethnic Russians would have the blessing of the government to rob, rape and murder the Jews living in their town or village. This is why so many Jews immigrated to the US and other places during that period. Communists are staunchly against Anti-Semitism in theory, and during the Revolution Jews were instrumental. For instance Trotsky (Jewish) was the top commander of the Red Army. Yet, after Stalin took control (check out "The Revolution Betrayed" by Trotsky) he brought back the Russian Orthodox Church and a certain type of nationalism with a historically Anti-Semitic bent. What happened in the USSR after WWII was that Jews were systematically discriminated against similarly to the way black people in the US are treated. Parts of my own family lived as Jews under the USSR and it was not great but also not terrible. Jews were second in line for jobs, subject to police bullying, micro-aggressions, etc. For Jews the 1917 Revolution was similar to the US 13th Amendment/Emancipation Proclamation - it freed people from unabashed government approved oppression and it was a million times better than before, but there was still a lot of discrimination (and still is in Russia against Jews and the US against black people). Therefore, you are right to say there was Anti-Semitism but it was much more about the history of the region than about the Communist government. In general, because Communists are openly against all forms of discrimination on the basis of sex, ethnicity, etc. things tend to get better for minorities when they take over, like it got better for Jews in the USSR than under previous regimes. Just as the US claims to have a legal system that gives the same treatment to rich and poor, black and white, everyone knows they fall short of their ideals. Saying Anti-Semitism in the USSR was "because" of Communism is similar to saying Racism in the US is "because" of Representatives Democracy. They are related in complicated ways but each type of discrimination is more about the history of that location.