In this instance it's rather unlikely that the church had any position on gay marriage that she could have been asked to agree to when she took the job. She's been in the job for 12 years, and paranoia about that is a very recent phenomenon.
This is a situation where the employer has suddenly required compliance to a newly adopted political campaigning position after the employee was in post. If Ratzinger Corporation can get away with it, presumably it's okay for Coors to insist that its employees join the KKK or else.