This is only a single data point, but my experience being high-functioning autistic is that years of causing awkward social situations has made me hyper-aware of when I’m making people uncomfortable. And that’s actually inhibited my progress in dealing with gender dysphoria, as my desire to fit in and be normal conflicts with the desire to transition.
The correlation is definitely there though. It’s a cliche that trans women work in IT, and of course that’s where autistic folks gravitate. I saw somewhere that gender awareness and autistic symptoms both develop in children at around the same age. It wouldn’t surprise me if they’re somehow related.