So without getting into specific cases, splits are usually a combination of problems, in which political disagreement is frequently a lesser factor (while being presented as the main one). A handful of people joining with totally different attitudes to a single issue can easily clash with everyone else, a massive ruckus blows up and it ends with everybody having to take a side. Or it can be as simple as someone with a lot of mates in the org having a really massive falling out with someone else with a bunch of other mates. Tensions can arise because the finances have gone awry, or a key diplomatic figure leaves, etc etc. These would all be small issues in say, Unite, but if six people in an org of 30 are pissed off that's a fifth of the membership, which is a crisis and, quite easily, a split. Which is also exacerbated by the knowledge that no-one actually has to be there. I could leave Solfed tomorrow with minimal consequence - can't say the same about a union branch.