It really is pretty simple. The courts have repeatedly ruled that Federal Aid can't be use to force Universities to teach specific political viewpoints or ideologies. The exceptions that exist are very narrow, and involve either (1) conduct that isn't speech or viewpoint, or (2) declining to subsidize specific activities in the case where this doesn't require Universities to adopt a specific viewpoint or ideology.

No doubt this Court will dispense with those precedents because it's not really a Court of law anymore. But that's how you make Federal funding work within the bounds of a nation that has a First Amendment.