Summary: Waste disposal in space can ruin someone's day. And their planet.
The world of Shanvar-4 was an unremarkable terrestrial planet, devoid of atmosphere and seismic activity. Unsuitable for conventional terraforming, it was instead settled by burrowing deep into its surface, powering continent-sized habitats with fusion reactors. It was among the first worlds to have a fully enclosed para-terraformed ecosystem, although few around the universe noticed. Even fewer cared.
Interstellar space travel was largely the domain of artificial intelligences, uploaded minds, and other infomorphs. The few organic or material beings were primarily organics in cryogenic stasis, full cyborgs, or other augmented individuals able to deal with the massive timescales involved. Yet not all starships interacted with system authorities, owing to the gulfs of time and social drift between colonies.
Even in the Shanvar system, the governments of Shanvar 1, 2, and 3 were vastly different planetary governments. The outer system was host to ever-shifting constellations of habitats and fringe polities, many resistant to integration with the inner system. To the inner system, there was little worth in integrating such remote, artificial outposts. Yet both briefly found common cause.
The starship was a generation vessel propelled to a tenth of light speed. Based on its transmissions, sociologists estimated a cult formed from the descendants of the original crew. They did not cease to break as they approached the Shanvar system, although they slightly adjusted course. The single craft dropped another object, which broke off at relativistic speed.
The object was a stream of refuse, ejected from the underside of the craft. The relativistic trash impacted the four planets of the system, blasting Shanvar-4 the hardest. Its hardy settlements were saved from total annihilation only by their sturdy construction, but millions were still dead. Other debris struck wayward colonies in the outer system, killing untold sapients.
The body count was over two billion sapients. The survivors of the Shanvar impact took offense to the generation ship's reckless waste disposal. The outer system provided space infrastructure, while the inner system provided raw materials and personnel. Together, they launched a relativistic fleet of their own. They would avenge their system being treated as a trashcan.
That was how littering started an interstellar war.