It's likely common cause, rather than cause==>effect.
Something happens in the developing brain that is either a malfunction, or a wildcard switch. Either way it leads to a lot of 'minor' changes to the brain. It's part of the reason they half gave up exactly defining autism. It's a cluster of small changes that come as a group. Some useful, some negative.
The joke about the proportions of geniuses and the insane being lefties has some grounding in reality.
Interesting. It’s clear to me that gender identity is at least in part influenced by the culture around you. Maybe being less able to comprehend social expectations makes you less prone to conforming to the gender ones? Idk seems plausible.