Do you have stars as actors in 3d space or only as material on skybox?
If you have them on skybox only as bright dots on texture then i am afraid only postprocess will work if you want to have trails exactly where stars are.
However i think that best (and easiest to do) would be effect as this:
Use material for star skybox, add to there hue shift to modify final color of stars.
When your spaceship accelerates, use hue shift to simulate shift to purlpe color in direction you move , and hue shift to red behind you , and lower brightness of stars, so all your stars will shift realistically. For more realistic view you should “pinch” all uv coordinates on skybox in direction you are moving your ship. Then when ship gets to speed of light, do very bright flash of skybox at direction you move.
Above hue shifts and brightness gradients you can easily calculate from dot product of ship velocity vector and negative normal of skybox. You will get nice constant gradient, pass ship velocity (normalized) as parameter to skybox material.
After that (right when you do that flash of going to FTL) you may spawn 100 or so star emmiters with trails.
I think this is easiest way to make FTL trails without much immersion breaking artifacts. Anything else may be just complicated hax.
AS for trail particles:
You can use beams with zero randomness and very long beams (i think this is easiest on engine)
or use trails, or use lots of stretched i velocity direction dot particles (but this will use lots of them)
Also use “local space” for particles, with initial velocity, and pass that velocity as parameter or rotate emitter.
Spawn all stars randomly around from single emmiter, not 100 emmiters that each spawns 1 stripe.