So much for being the party of small Government.
The federal government doesn't have the Constitutional authority to use funding to coerce states into acting in a certain way unless it is
directly related to the specific funding being withdrawn.
That's why it was ultimately held that the federal government could not deprive a state of all highway funds simply because they wouldn't reduce the speed limit to 55, and why the Obama administration couldn't deprive states of all Medicaid funding just because they wouldn't agree to the Medicaid expansion. The only "penalty" that could be imposed was not giving the state's extra funds to pay for the expansion if the states were not choosing to expand.
If you think about it, that's a good thing. Otherwise, the federal government could coerce states into doing almost anything by threatening to deprive them of all federal funds unless they adopted a certain policy.
So for example, Trump's threat to deprive schools of all federal funding just because they have DEI programs would be unlawful. You could deprive them of whatever minuscule amount of funds the federal government contributes to anti-discrimination programs at schools, but that's it..
The right way to go after those DEI programs is to leverage the upcoming Supreme Court decisions on affirmative action to support lawsuits against any educational institution that teaches affirmative action or anti-white bigotry.