By "force them to do X" he meant the government can refuse to fund them if they didn't do X (which forces them to abide by the government's rules if they are accepting its funds), not that the government can legally mandate them to do X unconditionally.
Conditions placed on the recipients of government expenditures are not unrestrained by Constitutional limitations. Witness the Supreme Court throwing out some of the strings attached to ACA's Medicaid expansion.
You are going on tangent after tangent as if to prove something. No one said that "unrestrained by Constitutional limitations" are ok.
Suppose you have the right to exclude Blacks or Asians from your college (freedom of speech, associations or whatever)
Once you take even a penny of federal dollars, directly or indirectly, you may have to agree not to discriminate. So YOU give up that right voluntarily. No one forces you to take the government's money.
By "force them to do X" he meant the government can refuse to fund them if they didn't do X (which forces them to abide by the government's rules if they are accepting its funds), not that the government can legally mandate them to do X unconditionally.