Under what circumstances can a rabbl bring his own food, cutlery, crockery etc. to a non-kosher restaurant, while his guests partake in non-kosher food? If he can’t, what is the halachic reason for this?
Unless there are very extreme circumstances (which I can’t imagine), it would not be permitted for a rabbi, or for any other Jew, to eat in a non-kosher restaurant, even if he were to bring his own food. The reason for this is the principle of maris ayin, whereby an action that a person does gives the impression of a transgression, even when he is not doing anything wrong.
According to Iggros Moshe, maris ayin applies when “Someone thinks that I violated something, or he thinks that I inappropriately ate something non-kosher.” This would certainly apply to eating in the non-kosher restaurant.
Sources: Iggros Moshe, Orach Chaim 1:96, 2:40, 4:82; Minchas Shlomo 2-3:53