Update: Oct. 16
McCaskill says she's "not anti-gay" and feels that she is being bullied; WJLA news story here.
I would seem to me that she did not seek to draw attention to her own views by signing a petition, so there is no conflict of interest. The University should definitely reinstate her now.
This video, in sign language, says "Signing a petition is a civil right." It would seem to be guaranteed by the First Amendment, for a public employee (but this university is private, isn't it?)