Do Catholic hospitals have a right not to perform abortions?
Just a brief comment, which is that, even if one always does have a moral right not to do things one regards as morally objectionable, it does not follow that one has a legal or political right to do so, i.e., that one cannot legitimately face legal consequences for not doing so. It is fairly easy to come up with counter-examples by thinking of people whose moral views are themselves pretty objectionable. I don't know which issue the questioner probably had in mind, but both seem worth considering.
For what it is worth, I think similar such examples make Aquinas's view very doubtful. If one thinks a thing is morally abhorrent, say, when it is, in fact, morally obligatory, then it is not at all clear that one has a moral right not to do the thing. Indeed, it seems almost contradictory to say one does: One has a moral right not to do something that is morally obligatory? Presumably, the resolution of this "paradox" lies in distinguishing subjective from objective elements of this, as is now pretty common.