You do understand that there are creeps out there grooming children, right? Parents definitely do need to have oversight over their own kids.
Children should absolutely not have privacy on the internet.
The ID requirement is terrible, but saying that children need privacy to explore their sexuality on the internet is very problematic.
If this is the position the UK government holds then that brings into question their desire to protect children online in the first place.
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.
This discussion started from the categorisation error. Technical means should be irrelevant here.
However, as we have already seen, asking nicely in the HTTP headers doesn't actually work, it may even help porn peddlers better target children. We also know from recorded interviews with these predetors that they don't seem to actually mind exposing kids to porn.
This is a dangerous semantic drift that ignores how teenagers are in the process of developing into adults, and so need the parent supervision of them to be slowly relaxed. (Especially since, if handled poorly, they tend to rebel, and cause much more damage.)
And, as a reminder, not all erotic or erotic-adjacent (or other "adult topics") works are porn,
and depending on the jurisdiction the age of consent is often less than 18
(16 in UK, though I am sure there are important details hidden behind this single number),
though I do understand that there might be new, unique challenges here in the Internet era, with laws that might not have caught up yet.
They just want to throw responsibility and blame on parents, so that government dont restrict porn access. Parents are just a tool and scapegoats.
Sexuality is part of the human condition that doesn't start on one's 18th birthday just because over-protective parents want complete control of their child.
It's weird that parents believe they need to control every facet of their child's life, down to being able to learn about why they feel the way they do. It's a form of abuse and coercion.
What happens when someone wants to explore their sexuality by finding someone other than the pre-approved person from the parents?
That said, I personally think good parenting means giving children privacy, even online, and doing so increasingly at ages set according to the maturity/capability of the child. That's the sort of thing a parent is in a better position to assess than the government. I also think that this particular law is garbage. I just don't think "We must protect children from their parents by allowing them to access the internet in secret and anonymity" is a very compelling argument.
For some children their parents finding out they're gay would cause a great deal of real world physical or phycological harm. It's a really tricky thing to navigate, but aside from saying 'no children should be allowed access to the internet unsupervised' it gets really difficult.
