Unless his employer allowed him to opt out of filling scripts for birth control or there was a law that allowed him to do so, he would be required to fill all prescriptions.
And I'm not aware of any doctor whose job description requires him or her to perform abortions
I imagine that doctors who work at abortion clinics do.
A doctor opposing abortions would of course seek a job at an abortion clinic... NOT!
If his job description required him to dispense abortaficants, then I would tend to agree he may have breached his employment contract. I'm unwilling to jump to the conclusion in the absence of evidence that he breached his employment contract.
On the other hand I am sure that pharmacists have the discretion to refuse to fill prescriptions for a wide range of reasons. To suggest that they have a unqualified duty to fill any script handed to them is unreasonable.