Oholei Shem Siman 59 says that it is not proper to give a Mezuza to a non-Jew to place on his door, per the the Maharil, Kneses HaGedola, and Rishon L'Tziyon.
However the Sheyilas Yaavetz Chelek 2 Siman 121 seems to say that if the non-Jew will respect it properly then you may give it to him to put on his door.
The Igros Moshe Chelek 5 Yorah Deah 2 Siman 141 seems to diffrentiate between giving it to a non-Jew who will put it on his door and giving it to a non-Jew plain. By a door he holds it may be more stringent, since perhaps he will have a robbery and then he will be upset and throw the Mezuza in the garbage and therefore it would not be permitted, however to give it to a non-Jew who will take care of it properly and is not placing it on his door there it would be perhaps permitted.
To give an example from the "mimetic," rather than "text-based," world, President Chaim Weitzman famously presented a Sefer Torah to President Harry Truman. (Follow the link--there's a picture of the two of them posing with the Torah!)
The Jewish History Blog says "When Truman saw it, he said, 'I always wanted one of those.'"
Rabbi Berel Wein, who wrote that blog post, adds that "Weizmann presented Truman with the traditional gift Jews give to heads of state: a Torah scroll." Rabbi Wein is Orthodox, and presumably the traditional Jews were traditional.