I think the way to combat antisemitism and supersessionism is to recognize it comes in two forms (well, besides “hard” and “soft”): essentially (1) prejudice against human beings, and (2) theological supersessionism.
The first is combated easily enough through getting people to befriend Jews or hear their side of the story. This can also include educating people about the Holocaust and showing people documentaries, the human interest stories to ignite their pathos. Once you understand someone and their motivations, it’s harder for you to judge them negatively. Getting to know real, leaving Jews and also learning about Jews of the past and studying Jewish history is key in this regard.
Secondly is much more difficult. Essentially, to fully combat supersessionism, one must systematically dismantle supersessionist interpretations of Scripture through proper bible teaching and understanding context. One key part of this is education. As many of the comments above suggests, when a Christian finds out the view they’ve been taught is anti-Jewish or supersessionist, they will normally be shocked and realize that’s not the best view to have. Another key is context. So much of the Bible is read without context. And you don’t even need a Master’s degree in biblical interpretation to do so. You just have to be an astute reader of the Bible. When you realize that the whole Bible is about Jews, and every book of the Bible is written by Jews (and also for Jews, in many cases – possibly with the exception of Luke the physician, who may have been Jewish or gentile), and that Christianity is a Jewish religion, that is, a religion that originated inside of Judaism, the better. Gentiles who read the Scripture are actually looking at someone else’s scripture, but thankfully, Gentiles are grafted in to the commonwealth of Israel and are inheritors of the promise of Abraham, alongside the natural branches. When people begin to see this commonality and unity lived out as Jews and Christians walk together under Messiah Yeshua, lives will be changed.