Culture now is very international.
That being said, I think there are some significant factors in the US that can be resisted elsewhere. I work in libraries (not UK) and I have to say I think that in many ways US libraries have created a situation where just this kind of outcome was likely. Thirty years ago public libraries in the US were loved and trusted by conservatives and and liberals, but these days you find that conservatives often feel they have been made to feel unwelcome.
They've made a few major mistake, but the main issues is simply that they have abandoned all pretense of neutrality. It's both passive - due to the fact that something like 98% of American library workers are Democrat, and often the more left of the party, and so it's easy for them to be in a bubble.
But it's also explicit, a huge thing in American libraries now is an rejection of the idea that libraries should be neutral, the argument is that they should be institutions to promote social justice and activism. And the ALA has really run with that, to the point of often inviting Democrat political figures to their conferences.
You also see it at the library level with regard to collections. You will see a lot of complaint about right wing book bans, but the same people will openly say that they will not buy conservative books they don't like, because they don't meet the standards of being good resources. So they are not asking to have books removed - some of these books are not getting into these libraries in the first place (though there are certainly attempts from progressives in some cases to ban books like Abigale Shrier's Irreversible Damage, for example.)
There also IME tends to be a lack of perspective around book challenges, often treating them as if they are necessarily unreasonable. It's important to remember there is a reason mechanisms exist for books to be questioned, and most of those that come under scrutiny are in children's sections, where collection development guidelines state they should be age appropriate. I've seen American library workers argue that if a book is marketed to youth, moving it to the adult section because of a lot of sexual or violent content is censorship. you see the same thinking around book challenges in schools, even though schools have a different mission and set of concerns around appropriate materials, compared to public libraries.
All of this is to say, I think the attitude in libraries in the UK is far more sensible, and if they manage not to lose their heads, they may well find that American style activism doesn't get that far. If, however, they take a page from the American progressives and become explicitly political, they may well see the public become more sympathetic to such ideas.
P.s. I, like a lot of librarians, see it very much as a calling, and I've been dismayed for years at the abandonment of the basic ethos of libraries that made them so important to the maintenance of liberal democracy. And it really isn't the Republicans who started that shit. It's one of the greatest sources of my negative feelings these days toward political progressivism, they have let down the gates and destroyed institutions I love.