Civil wars arise from all sorts of causes, and they usually arrise very suddenly:
1) Simmering ethnic differences: A multiethnic community which is thrust together because of external forces can very suddenly erupt into war if those external forces change or shift or if the balance of power changes sufficiently within them. Example: Lebanon, Yugoslavia, Sudan, Syria, Rhodesia, Rwanda.
2) Economic Collapse: A sudden economic collapse brought about by a war, failed currency, or excessive debt can cause a populist uprising as deparate persons attach themselves to extremist groups promising relief. Example: France, China, Russia, Weimar Germany
3) Divergent Ideology: A community can splinter into two ideologically separated camps with incompatible interpretations of the facts and views of how life should be lived. Eventually without ideological reconcialation, this will lead to civil war. Example: Holy Roman Empire, England, USA
4) Succession Crisis: The fundamental institution of government is the arrangement for the transfer of power from one individual to the next. If that institution fails to create a clearly legitimate candidate, government collapses and there is little recourse but war if one side doesn't concede. Example: Rome (repeatedly), Arab Caliphate, War of the Roses
5) Nationalism: A portion of a larger empire can decide it would more efficiently rule its own affairs. Example: Holland, American Revolution, Haiti
And of course those causes can be mixed and complicated by many factors.
In the case of a Star Wars campaign, with the larger political structure of the galaxy in flux, there are an almost infinite number of reasons why individual systems could errupt into civil war.
Some Star Wars specific examples:
1) A planet could be colonized by two different human genestock lines. Superficially similar, they may no longer have the capacity to interbreed. There relative similarity has served to keep them neighborly, but it also makes them direct competitors for living space and resources. Turmoil for external sources may create a situation where the two species differences are brought to a fore and whatever accomodation they had falls apart.
2) A planet could be colonized by two different species. As
#1 , but they are more likely to enter conflict because one species suddently realizes tha the second species has control of something that it now wants. This could occur because the first species has recently increased its technological ability and for example, now wants to engage in borehole drilling, terraforming, climate control, or underwater mining/extraction.
3) Loss of external authority has recently placed greater strain on what was formerly a figure head government with little responcibility. This has produced a succession crisis. Personally, I've always wanted to do a civil war on Naboo, based on Lucas's superficially strange 'elected Queen' governance system, and its similarity to polytheistic figurehead Queens/Kings who are ritually sacrificed at the end of thier terms. Personally, I love baroque (or is that broke) poltiical systems. At the time of the prequels, the system seems to have stabilized into a fairly stable figurehead queen regularly transfering power with an actual ruling parlimentary system, but its easy to imagine all sorts of competing political views - Republicans that think the vestiges of the old sacrificial system is a sick joke and the Queen instituion should be abolished, Conservatives that want to maintain the existing system, Monarchists that want true power vested in the Queen, and religious cultists with primitive knowledge of the force that don't think ritually killing the old Queen after her term is up is quite good enough and would rather more blood was spilled to properly invoke the 'great wheel of life'. Suppose for example, the ruling governing party discovered that the next Queen strongly favored a rival parties platform, and decided that it was in the best interest to NOT end the term of office of the current Queen in a timely fashion so they ally with the small Monarchist party to rewrite the Constitution to make the Queen apointment lifetime.
4) Disruption of trade with the greater galaxy has lead to an economic collapse, resulting in the rise of some sort of extremist view point (radical nationalism, communism, religious fundamentalism) promising an easy to understand escape from the crisis.