Don't think Obama or Biden threatened to withhold federal funds. Big difference.
That's precisely what the letters said: that federal funding was contingent on following the policy outlined in the letter. Here is one of the letters: https://obamawhitehouse.archives.gov/sites/default/files/dea...
The linked letter reminds schools of their requirements to comply with civil rights statutes that have been on the books in the US for many years. The trump admin, otoh, is on a witch-hunt to “protect” conservative views based on their own feelings and concerns. Not the same.
Yes, every new administration can attempt to impose their will on institutions of higher learning (so long as the administration has some sort of leverage, like funding or legal threats). The wise administrations limit their imposition, preferring to allow academia to enjoy high levels of freedom, autonomy, and funding to achieve their mission.