I try to stay neutral as well.
Turned unfriendly to the Federation due to some crossfire incidents early after gamma release, and stayed like that for quite a while. Made a few missions, maybe ~3-5, but after that I just moved on. Eventually, by mostly bounty hunting and selling exploration data to Federation stations, I changed back to neutral again
Even better, doing the same for the Empire just earned me friendy status
I am too far away from Alliance space - haven't seen an Alliance system in months. Eventually I will have to make the trip, >200k bounties pending...