A series of studies in the 70s, I can't quite remember exactly where but I seem to recall it was at a university in Calafornia, were made on how people relate to babies, especially focusing on similar situation with babies of apparently different sexes.
When I worked in Obstetrics, I noticed that mothers, when they cuddled their daughters, while they were lying next to them, often tended to put their elbows over the genital area, but with boys this was less apparent.
One of the results of the 70s study indicated that women, generally, tended to cuddle girl babies closer than boy babies.
This may seem, on the face of it, to be social conditioning. But I suggest the way a mother behaves in this regard is instinctive. The effect on the baby, which is, at that stage, so dependant as to be part of the mother, is, I suggest, equal.
From my own perspective, to suggest that any effect on the baby is conditioning is moving into the realms of social reconstruction along the lines of 1984 or even the sifi Borg.
Mothers, whether we like it or not, are designed to care for their babies and give them the best start in life. In the same way that we are each designed to care for ourselves. Self preservation, for a mother, extends to her baby, because her baby is, effectively, still a part of her.
How a mother manages her baby is, and must be sacrosanct. Interference in this most basic function is unacceptable.