The courts have decided previously that the Federal Government can put conditions on the money it gives to the States. That's why we have a 21 year old national drinking age...the states wanted the federal highway money, and Congress wanted 21 to be the drinking age. Do X, and we will give you money for Y. Now, this is a fairly well known case that I haven't read in decades, so if I got something wrong about it, Frank will be here soon to tell you that I never went to law school. :-)
Granted, there is some contrary case law since then, so I'm not sure where we stand now on this. I'm not sure where the line is drawn now, or if there is even a clear line anymore. That's why it will be interesting to watch.
Issue: Can the government offer money to a party (state government, state university, private university, etc.), and put limits on what they do to accept the cash? I'm guessing the limit will have to have some nexus to the reason the money is given. But, different courts will have different positions on how tight the connection has to be. Is highway construction money really tied to a drinking age? Seems kind of a loose connection to me, to put it generously.
In today's hyper-political environment, where people can't think clearly when it comes to Trump (e.g., they often condemn things Trump does when they support the same things done by others...no objectivity...who would've thought the left would become anti-environmental terrorists...that suddenly they'd be concerned about inflation, etc., etc., etc.) ... but given that hyper-politicality, I would expect Obama appointees to be very tight with that nexus when Trump is in office, and very loose when the next Democrat is in office, which will create a lot of bad law.