Does the takkanah of Rabbeinu Gershom apply also to gentiles, with regard to the issur of opening others’ mail?
Some write that the takkanah applies even to non-Jews, but others have expressed doubt concerning the matter. When there is a need, such as saving oneself from potential damage, one may be lenient.
Sources: Chikekei Lev (Yoreh De’ah 49) writes a number of possibilities as to why reading another’s letters should be forbidden. One possiblity is because of the mitzvah to love one’s neighbor, in which case it would not apply to non-Jews.
However, another possible reason is on account of geneivas daas, “stealing another’s heart,” in which case it would apply to non-Jews (see Chulin 90, where the prohibition of geneivas daas is applied even to non-Jews).
Chikekei Lev concludes by quoting a third possibility from Torah Chaim (III, no. 47), who writes that the prohibition is on account of this being a type of theft. Based on this definition, Toras Chaim writes that the prohibition would apply even to non-Jews.
Yet, Chikekei Lev adds that when opening the letter is required to save somebody from potential damage, it would appear that the takkanah was never enacted, and it would therefore be permitted.
Rav Zilberstein (Chashukei Chemed, Yoma p. 55) writes that when he approached Rav Elyashiv about this matter, Rav Elyashiv replied that based on the reasoning of Toras Chaim, it would appear that the prohibition would not apply to non-Jews. Even with regard to actual gezel, Chazal dispute the application to non-Jews, and where there is no true gezel, but only an extension of it, there would be room for leniency.