I was once told that there's a crypt in the Old City of Jerusalem near one of the gates (I forget which one), which houses the remains of a well-regarded non-Jew (once again, I forget the exact details), but that this doesn't pose an issue of Ohel because Ohel doesn't apply to non-Jewish remains.
Having been a student at the time and certainly not an expert in Tumah/Tohorah, nor a Kohen, I took this as fact without questioning it, until such time as I could learn these laws (which I still have not; at least not significantly more than before).
However, as I mentioned in this question, the Chicago Rabbinical Council has published an online Chicago tourism guide for Kohanim. This seems irrelevant, if not silly, if the remains are not Jewish - and many of the issues of concern seem to be related to remains that are almost certainly not Jewish (Egyptian mummies and the like).
So now I'm wondering if Ohel with non-Jewish remains actually does pose a problem for Kohanim.
More broadly, what Tumah issues do and don't apply to non-Jewish remains?