My first thought when such claims are made is "how do they think brain development works?" The brain does not develop except in response to novel intense experience. If we were to shield children from exposure to language until age 5 when the language centers of the brain typically mature, the language centers of their brain would not mature. It is exactly the exposure to those things that they are "not ready for" that cause brains to develop at all. Without such exposure, the brain does not develop. And there are critical periods, as well, where the brain can lose the ability to ever develop certain facilities if not challenged. If you were to put an eyepatch on one eye of an infant at birth, for example, in order to protect them from the challenge of binocular vision until their visual cortex was 'mature' which usually happens 3-6 months after birth, you would guarantee that child would never be capable of mastering binocular vision.

The stress over the Internet in particular is doubly troublesome because of the profound and abundant safety of the Internet. Compare it to literally any other way of acquiring information and you'll see it's the only one that protects the viewer from having to directly and physically interact with other people, which removes almost all danger. Of course, 'almost all' is not 'all' and some people will reject even stupendous protection if it means there remains even a single sliver of risk. Those people I think can be dismissed out of hand because they are waiting for an impossible option to be presented to them.