This cure for Autism is broadly related to the leaky gut hypothesis of autism, rather infamously propagated by Andrew Wakefield in the 90s more generally and Jenny McCarthy more specifically went after gluten/casein in the 2000s. PETA made an infamous ad saying that milk causes Autism [1] because milk has Casein. This is to say that enough noise got made about this specific claim it got researched a bit.
Generally this diet has specifically been studied for autism treatment and the efficence of it's efficacy is very lacking for me [2][3]
This all being said, this doesn't necessarily mean that nobody can benefit from a casein or gluten free diet, there's simply insufficient evidence to say that people who avoid milk and bagels are autistic less often/less autistic.
[1] https://www.dairyreporter.com/var/wrbm_gb_food_pharma/storag...
[2] https://link.springer.com/article/10.1007/s10803-019-04266-9