I am skeptical. (especially after recently taking a College Nutrition course that was more extensive than is required of most physicians.) There are a lot of diet fads out there, promoted on the internet, which actually go against the most advanced and accurate scientific understanding. So I am skeptical of the anti-(insert name of food or nutrient) fads.
Some individuals have a gluten allergy, or dairy allergy, or are lactose intolerant. These people need to avoid these foods. But that doesn't apply to everyone.
I do think that some people eat too much wheat. This doesn't mean wheat is bad: it is good, but good diet is about balance, and too much (or too little) of anything is bad. Other people eat too few grains.
However, it could be that in some cases, some people end up replacing the wheat and dairy with something they already needed more of: vegetables, for instance. If that were the case, and this person started eating sufficient vegetables for the first time, because of greater health, their mood and stuff could improve. Which would be good. But that might not mean that gluten caused problems, it might just mean that they are now getting a vitamin or something that they had been deficient in.
I eat a mostly Dairy-free diet, but that's because I am lactose intolerant. After I discovered my lactose intolerance and reduced/eliminated dairy, there was no difference in my autism symptoms.
I did find I had more sustained energy after I started replacing a lot of wheat with brown rice. Currently I rarely eat grains. (I actually think people should eat grains-I don't but that's because of a taste preference thing.) I mostly just eat vegetables.
I don't think either of these changes affected my autism symptoms.
Healthy eating is about variety and balance.
No food type should be villainized.