I would have answered that having the baby is morally acceptable.
Having a baby is not a sin. The sex that preceded it probably was, unless the woman was forced - that’s not a sin for her, obviously.
But I don’t consider childbirth to be morally unacceptable.
The question is badly phrased. They should have asked if sex outside of marriage is morally acceptable.
Then later you said "They should have asked if sex outside of marriage is morally acceptable."
I'm guessing you think the answer is yes; having sex outside of marriage is morally acceptable.
Sex results in having babies. So if its morally OK to have them outside of marriage, then it must be OK to have the sex outside of marriage in order to have them babies.
"But I don’t consider (out of wedlock) childbirth to be morally unacceptable."
I do. Its morally and socially unacceptable.