According to the law:
"No Jew may purchase Christian slaves because it is abominable that religious slaves would be defiled by the ownership of impious Jews. If anyone does this, they will be subject to the statutory punishment without any delay." [CTh 16.9.5]
The Christian belief that Christianity has superseded Judaism even extends to personal relations: no Jew can be seen having authority or superiority over Christians. Of course, Christians are perfectly free to own Jews as slaves and even use their position to get Jews to convert to Christianity.
The existence of Jews may be tolerated, at least, but the purity of Judaism is not protected in the way that Christianity is.