But they have that information anyway. If they want to know which subscribers access porn, I'm sure they can find that in the logs, filters or no. Not that I think filters are a good idea, but it doesn't really give "them" any additional information.

And search engines and social networks already have that information too. And even if there wasn't a db to search one could surely equally query which domains they'd accessed either from their ISP or DNS provider or GCHQ.

"Darling, I just logged on to our Sky broadband account and it says here that our porn filter is off. Do you know anything about that?"

a households IP requesting certain sites != account holder specifically requesting porn blocker be disabled

No, but IP requesting certain porn sites \approx user wants to see porn => account holder specifically requesting porn blocker be disabled. The equivalence can be expected to almost always hold, because its simply the easiest way to account for the behavior. Thus the inital objection stands.

So the account holder is most likely to be responsible for ALL internet traffic on the account? That's clearly not the case

There are tons and tons and tons of reasons (tons) to be against the porn filters. "The government is going to tell people I looked at porn in order to assassinate my character" is one of the most far-fetched and ridiculous ones. If the government is dead-set on assassinating your character, then first of all, you have a much more serious problem on your hands than a lack of pornography, second of all they have far more effective tools at their disposal than "Hey, so-and-so, (maybe) wanted to see a boob once".

Logically not equivalent, for sure. Practically, in most cases they would both say the same thing. We're not just talking about household though, surely some individuals have Sky accounts too and looking past that particular ISP if you're asking for unblocking from your mobile then there's a good chance that you're viewing porn - it's probably an equally veritable indicator as that your mobile visited a porn site.

I'm going to go with 99.9% accuracy as my first guess.

No, requesting that porn be unblocked does not necessarily imply anyone actually looked at it. An IP requesting it does.

No but it necessarily means that the account holder took action towards accessing porn.

An IP requesting access to a porn site does not - ads can easily contain pornography, malware can use computers to access anything, and anyone who can connect to the network can be the one requesting the porn site.

There is very little you can determine in the real world from a public IP requesting a porn site