It’s not perfect, like an RCT, but the socio-economic and cultural confounds could be controlled for by blindly screening the children for ASD (rather than relying on diagnoses sought by the parents.) It would not be possible to control for biological or environmental confounds too easily.

The current anti-vaxer hypothesis is “too many – too soon,” so a dose-response study should be more than adequate to test it. It’s not “one vaccine is just as likely to cause autism as 10 vaccines.” So a fully-unvaccinated vs. vaccinated study is clearly not necessary. Though that will likely be the first excuse in the event the study is negative.