All political parties are coalitions, and that is why they have nappers in them. You only have to look at Christopher Chope for the Tories. In our (very) diverse society, it's almost inevitable. You exercise party discipline, but there is always someone who says stuff you don't want them to say.
Conspiracy theories? They abound in our world and people from all parts of the political spectrum believe in them. It's just that some seem to be 'acceptable.' People get taken in with them all the time. They are 99% complete bollocks, and this particular one is 100%.
The Labour Party has not covered itself in glory here. No one is saying they have. But don't kid yourself that a lot of people, not just Muslims, are, at a minimum, 'concerned' about what is going on in Gaza. Some are fucking angry. Some hate Jews. Most don't. Lumping everyone who has concerns about Gaza together as some sort of antisemitic Nazi is a very dangerous tactic. Not least because some of those with concerns are Jews themselves. This outburst, ridiculous and offensive as it may be, is but a symptom of that underlying concern. Which, I have to say, the top politicians are not addressing at all.