I don't think your parents or doctors necessarily have the say, and if they do, I don't think that's Church policy. If we're using "intersex" to describe people who have non-binary physical sex characteristics (I get confused by all the terminology), I think it's reasonable as an LDS parent to wait for the child to be old enough to prayerfully decide which gender they feel they are. At least, that's how I'd approach the situation.
That's a very rare approach, as far as I know. Intersex babies are way more common than most people know about. I heard (in a class) at the annual Utah Gender Conference that more babies are born with some intersex variation than are born with Down syndrome. If that's even remotely true, we probably all know an intersex person, but how many of us know of kids who are raised gender neutral to that extent for the first few years of their lives?
I'm given to understand that in most cases mom and dad choose the "sex" of their child at birth with guidance from the doctors. I do know of intersex people who then felt they were assigned the wrong gender and others who felt the construct of gender was just unhelpful to unmeaningful to them.
In fact, many parents of intersex infants elect to have their children undergo surgery to make their genitals look "less ambiguous" when those children are incredibly, incredibly young.
before my daughter was born this was something I worried about. I think it would be tough to make that decision! Gender is something complete strangers will ask about your child (with or without gender-signifying clothes). It would be tough to have that awkward conversation all the time! But it feels like cosmetic genital surgery is premature for a baby.
