The user of the "he or she" locution may justly be charged with inelegant expression, but in this age, where true elegance is widely regarded as an anti-Semitic hate crime, it merits no additional abuse. It is, after all, grammatically correct, and what is more, it mirrors the situation it names.
Though "she or he" is equally unexceptionable on grammatical grounds, it may indeed truly brand the user as a timid acquiescer to the Semitic zeitgeist. Still, if this is the only hoop a Trad Catholic has to jump through to get or retain a job that will support his wife and kids in these hostile times, then Heaven be praised! I number among my acquaintances some decent and honorable academics who hold their nose when they write such things because when they do, they are not backed further into the corner where the only choices are resignation or compromise with far graver matters.
Far and away the most objectionable locution of this sort is the very one that even a casual CI browser must notice a score of times a day: the "polite" use of "they," "their," and "them" in the thousands of situations where the syntax requires a singular personal pronoun or adjective. For example, to refer to a topic currently being aired ad nauseam, one would not be surprised to read such a sentence as "Anyone who thinks Pablo is an asset to the Resistance needs to have their head examined."
If I were king, one use of such a repellent construction would bring a heavy fine. Two uses would earn an unappealable firing squad at dawn—or at some rather more reasonable hour if I had an all-volunteer army whose enlistees preferred sleeping in.