What is interesting here is that drinking 'diet soda' actually decreased the odds for girls (though not reaching statistical significance) - that strikes me as an extremely odd finding. Their discussion of 'why' was not very compelling. I have a hard time thinking there's anything causative with such a disparity in sex.
I also noticed that adjusting for some of the larger confounders for autism (maternal age, SES) didn't move the needle much. I would expect there to be a much larger difference between adjusted/not-adjusted OR. Maybe there's other confounders lurking or the adjustment was insufficient.
It'd be like trying to do anabolic steroids while your natural testosterone is very high.
Receptor saturation (in this case, E1 vs E2; first pass metabolism turns E2 into E1) is something I had to learn out of neccessity because my endocrinologist didn't really do anything beyond loosely following ancient standards of practice (we don't have specialized gender clinics in Germany).