I'm a therapist. Of the 20+ kids w ASD and who've tried the diet, only 1 really responds to it well.
Of the ones who show mild improvement, most have some form of allergy/food intolerance/skin or gastrointestinal problems eg eczema, chronic constipation, chronic rhinitis. Most are just healthier ie they dont't fall sick as easily, so they are more attentive & able to attend lessons or therapy regularly.
One particular boy goes "high" whenever he eats bread, noodles or cake for a few days in a row. He becomes very impulsive and more rigid & increasingly withdrawn/stimming. It reached a point whereby he almost lost his speech. He's prob sensitive to a lot of food but we dont't know. His family is not very diligent in controlling his diet; his behv is always yo-yoing. 2 days ago, he was laughing non-stop, talking away & grabbing things cos he was excited. Today, he didn't laugh but was shaking in his seat non-stop after which he would pace about. When he finally calmed down about 1 hr later (by making him do threading), he was able to hold a decent conversation with his partner.
His allergy problem (rhinitis & frequent nosebleed, unexplained fevers) is moderate but the sensory integration disorder is quite severe. This boy is high-functioning, almost "recovered" from autism, until the gluten problem appeared last year.
For kids who are non-verbal, it's harder to evaluate the effectiveness of GFCF diet. But most dietary intervention work on assumption of nutritional deficiency or intolerance/adverse reaction.