The Netziv (in a responsa in Meshiv Davar) writes that one may teach the Torah shebi'Chtav to non-Jews but not Torah she'Be'al Peh. Of course, we know that that is pretty much impossible. Torah shebi'Chtav is often entirely misconstrued without the explanatory teachings of Torah she'Be'al Peh. I understand the Netziv to mean that even where the words of the Torah can be misconstrued, there is a reason why the Torah was written in the "misleading" fashion that it was. Some lesson may be learned from the literal meaning of the verses even when that meaning is not what the Torah wants us to put into practice. These lessons may be taught to non-Jews.

Of course, one can teach non-Jews anything that pertains to their daily lives, which includes Midos and Derech Eretz (such as Sichasan Shel Avdei Avos).

The Rambam (Teshuvah #364 in Frieman edition of Teshuvos ha'Rambam) writes that the prohibition of teaching a non-Jew is not because the non-Jew may not learn Torah. (Apparently, it is alright for him to learn as long as he is being taught by a Jew and not "grabbing" our Torah for himself -- which answers Tosfos' question here.) Rather, it is because he will torment us if he finds the Torah not to his liking. Based on this, he writes that it is permitted to teach Catholics the Torah (since they accept that our Torah is Divine and will not find fault in it) but it is prohibited to teach Muslms Torah (since they do not believe that our Torah is Divine, and they will torment us if they find fault in it).

M. Kornfeld