Surely the equivalent of banning book burning would be for Miller's opinions to be unlawful?
Unlawful - as in freedom of expression by burning books is prevented by the police or prosecuted by the state due to risks to public safety or because it is considered a hate crime?
If by "allowed" you meant not a criminal act, then yes I agree that the equivalent would be for Miller's opinions to be prosecuted as a hate speech crime. The conclusion reached by the independent lawyer hired by Bristol university as part of its investigation is that Miller's comments were not anti-Semitism or hate speech.
I was considering what is "allowed" in a wider context of censorship e.g. in relation to freedom of expression and especially academic freedom. The campaign to sack David Miller and preventing his freedom of expression got the support of over 100 MPs.
Bristol said in its statement that academic freedom was “fundamental” to the university and that it “take(s) any risk to stifle that freedom seriously” but despite Miller's comments not being hate speech, he “did not meet the standards of behaviour we expect from our staff” - in effect his comments were not allowed if he wanted to keep his job. Miller's lawyer said it would be a ‘test case’ which will have to first consider whether Professor Miller’s anti-Zionism stance is a ‘protected philosophical belief’, under the 2010 Equality Act - before it then considers whether the university acted lawfully in sacking him.
What is allowed seems to be constantly being "revised" based on the interpretation of different judges - as can be seen in the cases beliefs about transgender rights. I think freedom of expression should be more consistently applied otherwise it's confusing why one group's feelings are protected but another group is expected to suck it up.