Who should get to decide what can and can't be written in a book, if not the author?
There is literally nothing stopping Kate Clanchy or any other author from having 100% control over what is published in their book. (Obviously not counting libel/legal challenges, which does not apply here.)
Anyone in the UK can go to Amazon or any number of other platforms and self-publish absolutely anything they like, without a single word being changed.
If an author wants a publisher to invest substantial money in their book, they need to accept that the publisher will edit the book according to what the publisher determines is most marketable. This is an absolutely standard part of book publishing and something literally every writer, bar a handful of super-famous celebs, goes through.
If you want someone to invest money in you then they get a say on what their money will be used on. Not censorship, just the practicalities of finance and marketing.
How many negative reviews should it take to get a book pulped?
Her book was not pulped due to negative reviews. Stop inventing falsehoods.
Should there be a criminal law made for writers who offend their readers, or certain of their readers? Should authors have to undergo some sort of training before being allowed to publish books? What kind of punishment should there be for writers who offend their readers?
You are literally just making stuff up.
I'm interested to know how you would solve the problem.
What "problem"? The "problem" of authors who try to cancel and censor negative reviews? Or the problem of publishers being unwilling to spend money on authors who create scandals?
That doesn’t make her responsible for everyone’s actions in any situation that followed.
She flat out lied and pretended that she was the victim of a vendetta because she wanted to cancel and censor her own readers, simply because those readers had opinions that Kate found offensive, and Kate believed that opinions she found offensive shouldn't be allowed online.
If she hadn't lied - repeatedly lied - none of this would have happened.