I feel like everyone can decide on their own globally between Student/in and Studierende/n, without changing every individual entry. It's a style issue, as Resti is surely well aware.
But the PC-ness of the German may be the least of the problems. Since the Studentenwerk seems to be where students can get help with things like housing, finances, counseling, and so on, past discussions have suggested things like student services (building) for it.
Just to review, in AE, the student union is the building where students hang out, the central location for all students on campus. It might contain a cafeteria or café, yogurt shop, post office, gift shop, reading room, meeting rooms ... or just comfortable chairs in a big lobby.
There doesn't seem to be a very close equivalent to that in German. One person from Göttingen suggested Mensa + Foyer in a past discussion.