Rav Haim Palachi (Turkey, 1788-1869), in a number of his works (Leb Haim, Ruah Haim and Kaf Ha’haim), cites a source from the Zohar indicating that gentiles transmit Tum’a (the Halachic status of ritual impurity) even while they are alive. As such, anytime one touches the body of a gentile, even if he simply shakes the gentile’s hand, he must wash his hands to rid them of this status of Tum’a.
However, the Peri Megadim (Rabbi Yosef Teomim, 1727-1792) noted that the widespread practice is to be lenient in this regard, and not to require washing after shaking hands or having any other contact with a non-Jew. The reason is that the formal Halachic status of ritual impurity is something that applies only to Jews. Tum’a has the potential to surface only when there is Kedusha (sanctity), and thus only Jews, who are endowed with the status of Kedushat Yisrael, are subject to the Halachic status of Tum’a.
As a practical matter, it would of course be very difficult to wash one’s hands after every time he shakes hands with a gentile, and one may therefore certainly rely on the prevalent custom not to require hand washing. Of course, one who can follow the stringent view of Rav Haim Palachi may do so, though obviously this should not be done publicly, in order to avoid enmity and ill-will between us and our non-Jewish neighbors and acquaintances.
It should be noted that one who, for whatever reason, goes to a non-Jewish cemetery must wash his hands after leaving the cemetery.
Summary: One must wash his hands after leaving a non-Jewish cemetery, but washing is not required after touching a living non-Jewish person, such as after a handshake.
