One of my pet takes is that WHF doesn't have religious organizations, because "religion" as a category is a concept that mostly took off IRL after the European Wars of Religion which redefined the word, and WHF hasn't had a similar event. "Cult" is a useful reminder that this is not a present-analogue world.
Have not many of the Empires civil wars involved mass cult on cult violence? Sorry I've been learning very much the hard way that innumerable wikidives and tons of quests and lore videos are no substitute for the ''first hand'' sourcebooks however deliberately contradictory they might be.
Sure they have. And lots of other bits of IRL history involved cult on cult violence too.
But to very crudely summarize a long and complicated history, what makes the European Wars of Religion such a turning point in our history is a combination of
1) stalemate and truce, usually in a war one side wins and might want to do it more after a rest, while the other side loses and wants revanchism if they still exist, but here the Leagues spent millions of lives to end up in a situation of "you know what, let's
not do this again, it was a complete waste of half our military-age males"
2) the Peace of Westphalia arrangement with the declaration of nation-states to mostly recognize one another as the rightful sovereign political actors on the world stage against non-states, where previously you might find a proto-state being invaded by something like a multinational labor union
3) the other Peace of Westphalia arrangement with the invention of state religions tied to the nation-states setup as a way of keeping the peace, the sort of compromise that leaves everyone similarly disgruntled, also leading to systematization and official legibilization of religions
4) European powers being on the rise at the time international world travel becomes practical so they can impose this model on everyone else (not as directly relevant to the Sigmar's Empire part of the analogy)
To expand a bit on points 2 and 3, before the EWoR+Westphalia turning point, it was common for the laws of a region to vary based on
which cult you belonged to, and not just in a "privileges for the ruling cult" sort of way. You know how Jews are not supposed to work on the Sabbath, for example, while Muslims are not supposed to drink wine? There were early states where these two rules were simultaneously enforced by the state apparatus against only members of the respective religion.
Again, history is big and messy, everything has some obscure ancient precedent if you stretch hard enough -
But with that said, EWoR+Westphalia is mostly where we get the modern idea that "a state" is the proper entity to have a code of law enforceable with coercion, as opposed to the Smiths' Guild being able to fine or flog smithing apprentices, and likewise "a state" is the proper entity to have a "state religion" (which can be None) and choose how harshly to impose this, as opposed to every local cult running around doing vigilante enforcement with varying degrees of coercion.
Like, if the Democrat Party wins local elections in California and begin passing Democrat-aligned laws that apply also to the Republicans there, we mostly accept that that's just how the political process works.
Prior to the codification of "religion" as a special case above, it was a lot more common and accepted that sometimes the Catholic Party would win local elections and use its political power to impose Catholic-aligned laws that apply also to the Protestants and atheists there, that's just how the political process used to work.
And that, I figure, is how the much of political process in Sigmar's Empire still works. The Sigmarites and the Ulricans have mostly backed off from the open bloodshed and settled to grumbling at each other, but both cults still play that sort of game of trying to get leverage to compel each other and trying to become the dominant cult in the Empire. Fear of retribution and national brotherhood can check them somewhat, but there's no meme of "it's wrong to mix
religion cult and politics", that would be as absurd to them as saying "it's wrong to mix political party membership and voting".