Feud between Star Trek and Star Wars lifestyles, lasting since the Atomic Age.
The Trekkist-Jedi conflict extends back to the late Atomic Age, when the film Star Wars was released. The Star Wars meme, ostensibly "science fiction" though really owing more in construction to the works of Atomic Age fabulists JRR Tolkien and Joseph Campbell, took root quickly and firmly in the minds of the baseline youth at the time. This put it into direct conflict with the older and more established Star Trek meme, which also had a resurgence with feature films released at roughly the same time.
By the early Interplanetary Age both Star Trek and Star Wars had developed large masses of devoted followers, and the conversion from simple fandom to religion/philosophy was proceeding apace. The Trekkist Church had by this time been founded, and the Star Wars groups were in the process of coalescing into the Jedi clade.
Both groups invested heavily in interplanetary colonization, building habitats and planetary colonies whenever possible. At this point, the rivalry between the two groups consisted mainly of spoof attacks on "enemy" computer networks, nasty insults, and forcible conversion of nonaligned rivals (see Scientology, Church of).
During the Nanoswarms in Sol System, the rivalry became an open conflict between the two groups. Black-market weapons and specially-designed "superweapons" were employed by the Trekkists and the Jedi, each determined that the other would not survive the swarms. Eventually, though, the swarms forced the combatants back behind their blue goo defenses.
An informal truce was called in the pre-Federation era, as both groups recognized a need to aid in the reconstruction of Sol System. The groups were also bolstered by the Expulsion; as billions of humans were thrown off Earth by GAIA, many were welcomed into the Trekkist and Jedi ranks. When the Federation was founded at Roddenberry Habitat, the Jedi perceived that any chance they had at gaining supremacy would not succeed, and decided to find their fortunes in interstellar space. The hardliners of the Trekkists also decided to leave the workings of the Federation to the willing-to-compromise moderates, and followed the Jedi into space.
Both groups founded planets near the edge of the Inner Sphere; the Trekkist cladehome of Vulcan, and the Jedi cladehome of Coruscant. From there the clades built up numbers and expanded further into the periphery, exploring and colonizing a number of systems. The rivalry was mostly forgotten during the Federation Age due to the general lack of timely communications between the two clades. However, the ancient feud became part of both Trekkist and Jedi mythology, especially the brief war during the Nanoswarms. It is believed that the disappearance of several Trekkist ships rimwards of Pacifica is due to an encounter with Jedi warships, but this has not been verified.
The invention of wormholes and the beginnings of the modern Nexus brought the clades back into full contact with each other in 4537. The reconnection brought back attempts at network attacks, but by the end of the 46th Century the "war" had dropped to a steady-state of insults and debates over religious minutiae. This steady-state was to remain the status quo between the Trekkists and the Jedi until the Version War.
The war between the clades flashed hot during the chaos of the Version War, when a Trekkist armada made an assault on Coruscant, causing massive damage to the world-city and killing billions. The Jedi retaliation sparked a number of smaller conflicts as anti-Trekkist factions took the opportunity to strike at their enemies, and the war was engaged. Aside from the initial blows, once the wormholes were closed casualties were fairly light, consisting primarily of the crews of the warships. Still, the Trekkist-Jedi War was one of the last of the Version War conflicts to be ended, finally coming to a halt with a Negentropist-mediated settlement at Roddenberry Habitat some 150 years after the Version War itself had ended.
Since the War and the reestablishment of the Nexus, the clades have returned to their steady-state of mutual dislike. As a sop to relativistic crews who are returning to the cladehomes from the war era, special virch environments have been constructed to simulate a continuing war between Trekkist and Jedi using "proper religious physics" (i.e. the nonstandard physics of the original fictions). These virches have, against all odds, become slightly popular in the Nexus, and are considered cult classics.