Barrett didn't act as a liberal, or compromised or blackmailed. In this case she acted as a true "Constitutionalist".
The USSC was asked to review the appeal's court denial of an emergency stay of the University's mandated vaccine. The appeals court based their decision on a previous USSC ruling that vaccines are a state issue (which they are, as are lockdowns, masks, etc).
Finding no issue with logic or use of prescedent, Barrett allowed the appeal's court decision to stand. This is how the USSC review process is supposed to work.
The plaintiffs are free to try a different track.

The problem is that:
A) this is not a vaccine—it is gene therapy, untested in human trials.
B) this is an emergency use authorization medicine, thus it CANNOT be mandated by anyone. It falls under the Nuremberg Code, which is codified in Federal law, making this ripe for consideration.
C) a decision could set a precedent affecting millions whose schooling and now livelihood is being threatened by out of control labcoat wearing technocrats.
Under any definition, this is NOT a vaccine.
Words mean something, and so should the law.