Can Colleges and Universities Require Student Covid-19 Vaccination?
TLDR; We say "Yes".
"moreover, many of the COVID-19 tests that colleges and universities have mandated in recent months have themselves been authorized under an EUA and not a full approval. For these reasons, we believe that our analysis — suggesting wide latitude for colleges and universities to mandate COVID-19 vaccination — applies whether the vaccine is approved or merely under an EUA."
by I. Glenn Cohen and Dorit Rubinstein Reiss
https://blog.harvardlawreview.org/can-colleges-and-universities-require-student-covid-19-vaccination/