all starting char's are neutral, its only if you choose to be an imp or reb that you cease to be neutral.
there are 3 neutral factions to choose from if you decide to stay neutral,
Freelance aka Pirate - semi affiliated with the Rebellion.
Corsec - affiliated with neither the Imps or Rebs
RSF - Loosely affiliated with the Imps.
Even if you choose to be Imp or Rebel, you can still chose one of the neutral factions as a pilot.
Its worth remembering, that if you decide to be an imp, and learn imp piloting skills, but later on decide joining the imps was a mistake, dropping your allegiance to the imps would also cause you to lose all your pilot skills. the only exception being, if you had chosen to be an imp but in space one of the neutral factioned pilot skills, then you wouldnt lose your pilot skills.