I think that “O come, O come, Emmanuel” is antisemitic in the same sense that the New Testament is at times antisemitic. It projects Jesus as the Jewish messiah and as the savior of Israel, which in it’s own sense perpetuates the antisemitic idea that Jewish people need to accept Jesus. I don’t necessarily think that we should ban “O come, O come, Emmanuel” however that we should be critical of it’s lyrics.
One of my seminary profs with a strong interest in Jewish/Christian relations shared these alternate lyrics to the song. They shift the perspective away from the supercessionist vision of “incomplete israel” and include more positive references to God’s saving actions in the Hebrew Bible/Old Testament. First verse and refrain below:
O come, O come, Emmanuel
And with your people always dwell
Who mourn in mortal exile here
Until the Lord of Life appear.
Rejoice! Rejoice! Emmanuel
Shall come again and with us ever dwell.