I visited a friend's house for NYE and he let me have his WiFi details, the parental filter option kicked in immediately even though he'd already chosen to not opt-in. Every new device that was added (and there were a few, as we arrived as a party staying for a long weekend) had to go through the same opt-out process.
Therefore, and with only this limited exposure to the system, I would guess that the preference is stored by MAC address per BT customer.
Unless my knowledge of network hardware is way off, MAC addresses are only relevant on a LAN - the ISP should know the router's MAC address, but not anything behind the router.
If the routers are cooperating with the censorship, they could be stored that way, but that seems like a lot of routers to patch (unless this feature was there from the start?)
If you visit the page for "Parental Controls" then right at the top is the picture of the Home Hub router and the "No software to setup"... because it's your connection that has the filter rather than local software:
From appearances this looks like a per-customer opt-opt, and then if opted-out (unfiltered ... well, still Cleanfeed) then it goes down to a per-device opt-out.
Most major UK isp's provide their own routers. While for most of them you should be able to use your own router, most people don't. Sky at least provides a router that is Sky branded and running Sky specific software - I would not be surprised if it does automatic software updates.
Most ISPs use configurations which expose connected devices and their identifying information to the ISP. There was a good thread on it yesterday but I don't have it saved.
The major ISPs in the US, in my experience have always allowed either opting for a straight modem instead of one with router/switch/firewall, or at least let the customer set bridge mode so it's passthru.
If this is ever not the case, it ought to be a big story and controversy, because the subscriber then could not get the connection entirely under his own control (and two firewalls and/or double NAT can cause problems).
That was the main thread in the discussion yesterday -- you're renting access to the provider's network and the endpoint connection hardware is a part of that. Even if you buy your own modem, the configuration is controlled by the ISP through the setup and the router (again, even if it's yours) will also be configured to allow some backdoor information for the ISP. I may be misremembering a bit of that.
I visited a friend's house for NYE and he let me have his WiFi details, the parental filter option kicked in immediately even though he'd already chosen to not opt-in. Every new device that was added (and there were a few, as we arrived as a party staying for a long weekend) had to go through the same opt-out process.
Therefore, and with only this limited exposure to the system, I would guess that the preference is stored by MAC address per BT customer.