If you work as a pharmacist, OB/GYN, or medical-surgical nurse, there’s a chance you’ll be involved in abortion or contraceptive care. And you need to deal with that. If you don’t want to deal with it, pick another medical specialty.
Doctors (along with the rest of us) sometimes seem to forget that the Internet is a real place with real consequences. The things you say and do there matter, and putting something up on a public Facebook post is like standing on a street corner and yelling.