Person B has two morally acceptable answers to this question, they can either say "Yes, I believe abortion is morally wrong" or "No, I don't believe abortion is morally wrong."
Why would you assume that these are the only two morally acceptable answers?
An equally morally acceptable answer would be It depends which is neither yes nor no.
This answer indicates that they have no interest in ethical discussions in society
No it does not. I don't care could also mean that the person is lacking the capacity¹ to form (or have) an opinion on this matter. It's definitely not a conclusive statement at all.
¹ by "capacity" I mean any capacity, like time or means to get to information etc. not just mental capacity.