There are studies which show that usually only one parent will develop this extremely light sleep to care for the baby. The other will be able to sleep through. Often it is the woman who will wake up easier. But it isn’t tied to gender.

Interestingly when homosexual couple adopt infants one of them will develop the same light sleep while the other won’t. Usually the parent who spends more time with the child will be the one to wake up iirc. Thought that was super interesting.