Biden and Obama found all kinds of ways via Title IX to invent rules. I’m pretty sure one can be invented for this.

Or are you asserting that Haaahvaahd has a right to federal research money?

Yes, they do. Or rather, they have a right for the same opportunity to apply for federal research money free of unconstitutional conditions. The government can't require you to abandon a constitutional protection or right as a condition for obtaining a federal benefit, even a discretionary one.

So, for example, the State of Florida can't require that anyone who wants to have a driver's license has to issue a written endorsement of Donald Trump for President. Getting a driver's license is a discretionary benefit - you don't have a right to get a driver's license. But they can't violate your First Amendment rights as a condition of letting you get it.

If there's an actual statute (like Title IX) that governs the University, then they have to comply with that law. But I'm pretty sure that many of the demands made by the Administration (like having more conservative voices) don't fall within Title IX.