As usual, there is insufficient information in the BBC article to tell us exactly what is going on.
If they're taking the books out of the children's section to vet them for age-inappropriate content, with a view to transferring them to the adult section or to store if they aren't fit for purpose, then fine. Given the dubious nature of some books and school teaching materials in this field, and their uncritical adoption in many cases, it's probably a very wise precaution. Previous due diligence can't be assumed.
But if they're going to censor pro-gender material from the library as a whole, then no. That's a slippery slope which sets a precedent for ideological censorship in other subject fields as well; and for censorship in the other direction if the political mood changes when people find out that Reform, too, have feet of clay.
We've heard enough on these boards over the years about attempts to silence gender-critical authors, using those very same arguments of "making LGBT people feel unsafe". It's not censorship per se the activists object to! But librarians should object to it and the rest of us should support them.