I've been speculating about this recently. I watched an old episode of Upstairs Downstairs from the 1970s, set in Georgian England between 1903 and 1930. I used to watch Downton Abbey. I've also followed the sci-fi series Bridgerton, set an alternate Regency era (see Bridgerton' is an alternate universe fantasy that sci-fi fans will love).
Watching those shows it's easy-to-see that pronouns really aren't new. Indeed individuals, certainly of the upper classes expected to be addressed by the 'lower' classes in a particular and set manner, at least until the 1960s. Heaven help a parlour-maid if she addressed her mistress with the wrong pronoun, and in Dickens novels, pronoun usage is manifested as a means to ensure the lower classes know precisely who their 'betters' are.
So is insistence on pronoun usage really that new? I posit that it isn't. Whilst demanding pronouns might have declined over the last few decades, I believe the current younger generation are demanding and indeed attempting to enforce their return in an effort to distinguish between themselves and the 'lower classes'.
Ok, it might be snobbery, but it isn't really the New Snobbery that David Skelton refers-to in his book. Rather it is simply a return to an expression of entitlement that was strictly-enforced throughout British history and elsewhere in-the-past.
I doubt that those who insist that pronoun usage be enforced and if necessary policed would be grateful to see acknowledgement that they are simply echoing the classism and privileged entitlement expectation of past centuries. Nonetheless I think such people should receive recognition that they are resurrecting a past tradition that is well-documented in British history.