> of course doctors should not be forced, that's ridiculous, but the SSN should prioritise hiring non-objecting doctors, at least in areas where there isn't enough coverage (in the same way it should prioritise hiring other specialities as needed).

I agree, they should!

But what do you do if your society just does not have enough people (nevermind doctors) who share the beliefs of pro-choicers?

At the point where you cannot find enough people to carry out an order for one side of an issue, it's a signal that the society itself has already taken a stand on the issue.