Interesting point, fitzy, which I don't think anyone else has elucidated so clearly.
I am still left with the feeling that even if KL is wrong historically and believes things that are mistaken, a move to stop him saying what he thinks is wrong. How will we know what stupid and/or wrong ideas people hold (about anything, not just Hitler) if they are not allowed to express them? How can we fight such stupidity and wrongheadedness if we don't know what it is because nobody can say it?
Does the Labour Party feel that KL is somehow speaking "for the Labour Party" rather than for himself? That is the only reason I can think of that would justify his expulsion from the Party. There must be lots of political party members in all political parties who hold equally daft ideas about a whole range of subjects.
The other thing that worries me about this episode and similar episodes where the whole argument against something someone has said is that it is offensive. Saying, in effect or actually, "you can't say that" is, quite simply, just as stupid and wrongheaded as anything. Argue with facts, with reason, with, you know, arguments. I'm offended is not an argument; it's a whine.
We should hear things we find offensive. We should hear things that make us doubt previously held beliefs or views. We should learn how to win an argument with reason, not with complaining. It's good for us to have our thoughts, beliefs, views and ideas challenged. 'Safe', verbally offence-free spaces are silly.
Disclaimer: this is not a defence of physical threats of violence.