So was Mahmoud Abbas anti-Semitic? It depends on the week really

The state of Israel does not really care about fighting anti-Semitism and it has no qualms about welcoming anti-Semites provided they give support to Israel.  That was true of Sadat and true of all the Western anti-Semites (from Balfour on) who are celebrated by Israel for their support of Israel.  Take Mahmoud Abbas: one week Israel remembers that he is an anti-Semite, and when he serves Israel well, his anti-Semitism is forgotten.