A private university can take away your scholarship for a social media post, not exactly a difficult thing to do. A scholarship is not some "god given" right. They have a vaccine policy that they don't need to make exemptions for. There's tons of legal ways they can do this.
A private university still has to adhere to discrimination laws for admission.
Man, you don't know when to stop, huh?
From the BYU-Hawaii Website:
"Student with a disability has:
...
- The right to participate in the university experience without fear of or experiencing discrimination due to a disability.
- The right to reasonable and appropriate accommodations to ensure equal access to programs, services, and activities."
Any physical or mental medical condition falls under the definition of "disability".
By their own policy, they have to allow her to attend.
This is in their admissions policy:
In compliance with applicable state and federal nondiscrimination laws (e.g., Title VI,
Title IX, and Section 504), BYU–Hawaii will not unlawfully discriminate against applicants
based upon gender, race, creed, religion, national origin, age, or disability who meet the
requirements, who agree to abide by the BYU–Hawaii Honor Code and Dress and
Grooming Standards, and who are otherwise qualified based upon available space.
The new admissions rule requiring COVID vaccine proof is in conflict with common sense, science and the law.