SCOTUS has routinely struck down prohibitions against the same things in other media, including explicitly the internet.

This isn't the right way to frame the question. The Constitution prohibits government actors from infringing upon the right to free speech[0], including that of children; meaning e.g. an attempt to censor a child's treatise on some subject would be as illegal as doing the same to an adult. It's not that you get a "free speech license" when you turn 18. The restrictions on government power applies whether or not the person being infringed upon is a minor or an adult.

[0]: This isn't an absolute, unqualified right. A child breaking into a profanity-laden tirade in the middle of class at a public (meaning taxpayer-funded and an extension of the government) school may believe they are exercising their First Amendment rights, but the school may still legally send that child home, for example, on the grounds that it disrupts the schooling of other children.