There are canons barring Christians from Jewish doctors, but it has to do with two things:
a) Jewish doctors were often the 'go-to' guys for abortions (they would, interestingly enough, perform abortions on non-Jews but not on Jewish women)
b) Jewish doctors often were involved in ritual magic as part of their art
If you look around for archeological evidence, you find a lot of Jewish magical papyri and amulets in the Byzantine world. I have several books on the topic I collected while working on my MDiv thesis on the Evil Eye. Anyway, it was creepy stuff, and so a canon was adopted to urge Christians to avoid
magicians Jewish doctors.
These days, I'd say it would be hard to find any licensed doctors engaging in witchcraft, though the abortion thing is still a problem. And, yet, with specialization, it is less so.