I have no idea what's going on inside Ken Livingstone's head. However, I suspect he's said, however undiplomatically, what some other people think,
In some ways there are parallels between what Palestinians are now experiencing with what Jews throughout history have suffered. The Israeli state discriminates against them and confiscated land which had been in Palestinian families for generations.
We read all the time about people not wanting immigrants. How would it be if thousands of immigrants descended on us and, in some cases, took over our villages and farms by force? I don't think many of us would be happy, especially if they were of a people we had historically disliked intensely.
I'm not going to get into a discussion about who legitimately 'owns' Israel based on ancient history. We all know why the state of Israel was created. It's there now and somehow or other people need to live together. It seems that the current Israeli leadership doesn't want to compromise and/or find a 'two state' solution and has expansionist ambitions. I don't suppose Gazans would have voted for Hamas if Israel had been more conciliatory, so now there's an impasse.
All of this has spilled over into global politics and has become muddled with historic stereotypes and rivalries. Livingstone isn't the only one to have conflated a number of issues. I have read that Labour supporters find it difficult sometimes to see Jews as victims, because (unlike other victims) many of them are very successful - hence the stories about Jewish conspiracies and the rest of it. I think there may be at least a grain of truth in people not seeing Jews as victims.
Whatever the reason for what Livingstone has said and done, he should have known how damaging it would be for the Labour Party, especially with all the accusations of antisemitism flying around. However right he might have been about what he said, he must have known that it was inflammatory.