While the Rambam holds that non-Jews are not Mitamei B’Ohel, Tosafos (Bava Metzia 114b at the top I believe; it might be 113b) says that he hold like the Chachamim over Reb Shimon. The Shulchan Aruch Paskens like Tosafos but makes it sound a little like a Chumra. (Rav Schachter is fond of quoting humorously the Macklokes between the Beis Yosef and Bach ere. The Beis Yosef says we can hold like the Rambam, especially because the Zohar agrees with him; the Bach responds that the Zohar is just R’ Shimon in the Gemara L’Shitaso. Jsut because he is quoted in 2 Seforim doesn’t give his opinion double weight.)
The accepted position of most is to be Machmir; though there are (rare) exceptions and Kullos given. As an interesting aside, the Avnei Neizer (I believe, not positive; might have my SHUTIM mied up) quotes a Ramban (Parshas Pinchas) that Kivrei Tzadikim are not Mitamei and therefore Kohanim should be allowed in the Ma’aras Hamachpeilah. One of answers given (I apologize, I do not recall by whom) is that Esav’s head is in the cave too.