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.