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For example, how about a law that says websites have to restrict access to pornographic content if the client's user agent sets an HTTP header indicating they don't want to see it? Now you don't have any privacy problems because the header contains no personally identifying information -- you don't even have to be under 18 to opt into it. But then parents can configure the kid's devices to send that header, without even impacting the kid's privacy to view content that isn't designated as pornographic, since the header is an opt-in to censorship rather than the removal of anonymity.
Also notice that an academic discussion of sexual identity isn't inherently pornographic but is something that can require privacy/anonymity.