This is rather weird framing since usually an additional citizenship (especially one in a country like the US) is considered a valuable thing to have for your child. Usually people claiming birthright citizenship are weird are doing it because they also see it as valuable. It’s also woven into the traditions of New World countries.

Regarding your concerns, I don’t see why it is unreasonable to simply renounce citizenship later or just simply double check your travel itinerary during the late stages of a pregnancy. This seems like at best an unfounded concern.