Withholding federal funds from colleges for not cracking down hard enough on speech the government doesn’t like isn’t related to the first amendment? Or it is but it’s ludicrous?
The 1A is regularly used to decide cases about funding as speech; Rosenberger v. University of Virginia for example forbade U of V from withholding funds from religious news organizations on campus.
I am sure there are arguments that this behavior is within the bounds of the constitution but the 1A definitely applies.