Masechet Avodah Zarah, Perek Bet (Chapter Two), Mishnah Bet (Second Mishnah). The Mishnah says, Mitrapein mehen ripui mamon. You're allowed to receive medical treatment for your possessions from an idol worshiper. Your possessions means animals. You can go to an idol-worshipping veterinarian. Aval lo ripui nefashot. You're not allowed to receive treatment for a personal illness because you should be nervous that the idol worshiper will kill the patient. The concern is that he'll give him a certain treatment, possibly a certain drug, that will hurt him—kill him rather than heal him. This is only if you're dealing with somebody who is not a skilled doctor. But it would be permissible to go to a skilled doctor, who would risk losing his reputation and livelihood.
Ve'ein mistaperin mehen bechol makom, divrei Rabbi Meir. According to Rabbi Meir, you're not allowed to get haircuts from idol worshipers anywhere, even if there are other people around in the public domain, in the Reshut HaRabim (public domain), because the razor that the barber is using could be used to kill the Jew. VeChachamim (the Sages) omrim. In the Reshut HaRabim, it's permissible, but not alone with him. The Chachamim say that in a public area where there are other people around, you're allowed to get a haircut from an idol worshiper because there, they would be afraid to kill somebody with other people around. But in a private, secluded area, there is no permission because there, you should be afraid that the idol worshiper will kill the Jew in private.
Of course, we can't be talking about being totally in seclusion because, as we said in the last Mishnah, seclusion with an idol worshiper is not allowed. So what we're talking about here is a place where the idol worshiper and the person getting the haircut will be alone for a very quick, temporary moment. And for that moment, the idol worshiper could take out his razor and slit the Jew's throat. So that's the situation. Even then, the Chachamim would say you're not allowed to be getting a haircut from that type of idol worshiper.