After my moaning yesterday, it turns out there is a new (very un-obvious) feature on Pinterest.
Near the top right of the page is a little icon that looks like two people.
Click that, and you only see pins from people you actually follow.
This seems like the ideal solution - people can pick what they prefer.
(Would be even better if this kind of personalisation was at the permissions level - so you didn't need to give companies the permission to profile you, and then choose to not use it - still, it's much better than most companies, who force you to 'benefit' from their profiling whether you like it or not, in the name of personalisation.)