The birth skirt is an item used solely in the beginning sequence to represent the supposed point-of-view of a newborn baby.
The birth skirt is not obtainable through normal gameplay and can only be obtained with the use of console commands. It is only worn by the Lone Wanderer's mother during the birth sequence at the start of the game.
The birth skirt only has a female model, but both male and female variants are set to use the same model. Attempting to equip this as a male will result in the character's torso, arms and legs appearing as female.