The tweet quoted in the article is an interesting example of the primary principle of anti-vaxxing:
Bullshit baffles brains
It suggests that the dorsal vagal complex might be "activated" when a baby is in a restraining seat, and this could lead to autism.
This appears to be a distortion of a recent theoretical statement, by a Dr Stephen Porges, called the polyvagal theory. The vagus is the 10th cranial nerve, is multi-branched and is involved in a number of autonomic responses in the body. It is involved in the control of the heart and disgestion and also in sexual responses (Robbie might recall her interest in her earlobe a few weeks ago). Polyvagal theory suggests that the autonomic nervous system may be adaptive - not just reactive.
The vagus has dorsal (back of the body) and ventral (front of the body) branches. Polyvagal theory looks at the relationship between experiences which might be due to external events and the normally involuntary responses of the nervous system.
This antivaxxer appears to be suggesting that since a baby is restrained largely on its back in a car seat, the dorsal branch of the vagus will be disturbed/damaged/upset/activated (whatever). Therefore neural messages arising from the discomfort will result in damage in the brain and hence autism.
I am struggling to recall the neuroscience I did as an undergraduate the major part of a lifetime ago. I think that I follow Porges' reasoning, but even I can see that a perfectly reasonable scientific theory here is being distorted here to suit the mindset of people who are hostile to conventional science. The danger here is that when one nutter makes an apparently authoritative statement the gullible will accept it as valid.
I don't think that I have misrespresented polyvagal theory but I would be grateful for any necessary clarification.