UK: Doctors with consciences not welcome

The Royal College of Obstetricians and Gynecologists in Great Britain have determined that any nurses or doctors who oppose any form of contraception may not complete training and will not receive certification in the specialty:

Doctors who oppose morning-after pill on conscience grounds face qualifications bar

Guidelines confirm that doctors and nurses who oppose controversial emergency contraception on ‘moral or religious’ grounds cannot receive key specialist qualifications

This is very possible in the US. Take a look here at some fairly recent history of attempts to keep docs from practicing with a conscience.