According to Sathe N, Andrews JC, McPheeters ML, et al. Nutritional and Dietary Interventions for Autism Spectrum Disorder: A Systematic Review. Pediatrics.
2017;139(6):e20170346:
People do use try to use diet as part of treatment
... many families, if not a majority of families, pursue dietary and
nutritional approaches as components of treatment. (Footnotes 1–11)
However, there is little evidence to support its effectiveness - the Strength-of-Evidence (SOE) is generally rated as insufficient:
RESULTS: Nineteen randomized controlled trials (RCTs), 4 with a low
risk of bias, evaluated supplements or variations of the
gluten/casein-free diet and other dietary approaches. Populations,
interventions, and outcomes varied. Ω-3 supplementation did not affect
challenging behaviors and was associated with minimal harms (low SOE).
Two RCTs of different digestive enzymes reported mixed effects on
symptom severity (insufficient SOE). Studies of other supplements
(methyl B12, levocarnitine) reported some improvements in symptom
severity (insufficient SOE). Studies evaluating gluten/casein-free
diets reported some parent-rated improvements in communication and
challenging behaviors; however, data were inadequate to make
conclusions about the body of evidence (insufficient SOE).
(Emphasis added above.)
In conclusion:
Despite their widespread reported use, little evidence supports the
effectiveness of nutritional supplements or the GFCF diet for
improving ASD symptoms. Harms reported in studies were generally
considered mild, but the long-term effects of these therapies are not
well understood.
[...]
Even without a clear evidence base documenting safety and
efficacy, many families of children with ASD use diet and nutritional
approaches.