So I sometimes have issues about whether I'm "allowed" to take anti-Semitism personally, because I'm not "really" Jewish, just "of Jewish heritage" ...

Yes, of course you're allowed to take anti-Semitism personally! The people who are serious about being anti-Semitic don't draw much of a distinction, anyway.

[edit] I had this window open for a while, so I see that the conversation had already reached this point, but just in case you need more data: yes, you are.