Princeton is quite prohibitive:
https://dof.princeton.edu/policies-procedure/policies/consensual-relations-students
UMich has an elaborate exception process:
https://spg.umich.edu/policy/601.22
but:
The guidelines state professors should avoid any romantic or sexual relationship with a student and must declare it, if not, because any relationship would be considered a conflict of interest. …
University spokesperson Mary-Jo Barr told CBC Montreal Daybreak host Mike Finnerty earlier this month that the school can not outright forbid intimate relationships between instructors and students — only strongly discourage them.
“We explored the option of banning such relationships, but concluded, for legal reasons, we cannot prohibit such relationships between consenting adult,”
Back in the day, if someone graduated and became a GTA elsewhere, it was common for their SO to transfer their credits and finish their degree at the same U. This was rarely a problem, since the GTA was usually working with the freshmen hordes. I don’t remember it ever being an issue.