What has no mass but exerts force on objects?
Watch some Ghost Hunters/Breakers/Doctors/Writers whatever. Whatever the heck those things are they move shit around but don't seem to have any mass themselves. Someone should pull them over for breaking the laws of motion. You know what else breaks the laws of motion?
Before I continue let me just say there is about as much evidence (if not more) for ghosts as psionics, if you count balls of light in shaky video footage. There's plenty of anecdotal evidence and if you're going to allow psionics in your SF game, why not ghosts? Following is a rules agnostic setting in I dunno how many parts.
If you're going to allow them then put them to work. Let them move your ship.
Most of the life (if you can call it that) in the universe may be mostly unseen and unable to interact with us taking the form of Non-Biological Entities. NBEs might be the spirits of the departed. They might be spirits pretending to be the departed or they might be something completely alien. the only real way to interact with them is through psionics. While personal psionic shields are fairly high tech; installations and ships or small craft can be shielded holding the NBEs and using their unique powers to move through space without clunky rocket engines or huge propellant tanks.
Many government, military and business interests have a vested interest in keeping up the official assessment of NBEs being unintelligent life that manages to glom onto researchers and others' thoughts to provide a semblance of personality to allow interaction for unknown reasons. The idea of enslaving intelligent beings went out of style quite some time ago.
In this setting man moves out into the Solar system and then the stars using spirits to power his ships. Psionics are necessary to interact or combat the beings of the void. When a ship is well maintained there's little trouble, maybe you hear some chains clanking from the engine room or catch a glimpse of a black eyed little girl in a mirror. Your ship did pass maintenance check, didn't it?
In any case if not trusted psionics are still indispensable to space travel. Psionic crew may be restricted to near orbit or further and never allowed on the ground. Some of them bring their work with them and who wants that? Rumors persist that some people have struck bargains with old powerful and alien NBEs that give them incredible abilities in return or who can control NBEs directly. None of this makes being a psionic easier.
In the wild so to speak their powers are limited by the energy they can gleam from endothermic reactions, that sudden chill in the room or the holo viewer flickering. In a ship's drive they are provided the energy they crave and lots of it by the fusion drive and their rantings and fits channeled into thrust or to open jump portals.
Some ship crews use telepathic or trained dogs to track down spirits that have escaped their engines and aid the ship psionic in spirit wrangling.
Most of the time NBEs are happy to be given power and will perform as desired for more. Some spirits do mutiny or escape to seek revenge for their treatment. Such entities are far more powerful after months of absorbing power plant energies. Some of them have proven capable of taking over living beings using their psionic powers like old legends of demonic possession.