I agree, that's definitely a concern. They can exercise a lot of control at the college admission point. Even if state laws or constitutions permit a free choice in private school curriculum, that can be overruled by Federal judges (cf. homosexual "marriage").
On the other hand, with colleges in such desperate competition for students who can either pay tuition or fill a "minority" quote seat, they may resist any limitations on the pool of students from which they can recruit. There are always other directions to go when you start following the money.
They can but will they?
The very first standardized test that my children took were the GRE’s for graduate school. They had no high school courses whatsoever and never took the ACT or SAT.
I read that homeschoolers are highly sought after by the leading colleges. Why? Answer: Because they are well prepared academically and socially and cause far less “drama” for the colleges.