Having read another post here, I get an impresion there are some similiar thoughts - or at least variations on a theme (see Spoonthumbs postLinkage
ensuring the 'neutral' player does not suffer would be the key so i would suggest factional alliegance does not have a massive impact upon your abilty to travel through a given system, it just helps a bit. The security level of a system would be more influential.
Do you need to grind missions to get this 'faction' bonus?
I would say yes - its rather like having a extra reward for serving your employer. Neutrals of course could run missions for different npc factions and get 'ok' bonuses throughout space.
PC Alliances could also give this kind of 'faction' standing to their pilots as part of a contract bonus. An alliance would want to give these out sparingly (you dont want a traitor leaving your Alliance and having the abilty to zoom around your systems). Alternatively Alliance 'standings' in this manner might need to degrade over time, or might be adjustable by the alliance itself.