The virginal conception of Jesus is a dogma of faith. The Church is silent on what actually transpired during the process of birth.The details of His birth are unknown but it is a requirement of faith that Jesus was conceived miraculously.
The “hang up” regarding His birth has to do with the logical conclusion of His miraculous conception. It is not part of the faith to believe His birth was miraculous though it is required to believe His conception was.
It’s the hang-up surrounding the supposed miraculous details of his birth (light, passed through a window, not theough the birth canal, etc.) that gets me, not his conception. That he was virginally conceived does not require that somehow his birth had to be anything other than natural, including messy, like any other human birth.