Best way to change factions is to blast the living hell out of their enemies

Alternatively you could do loads of missions for your chosen faction or just get a huge wad of cash and bribe them to let you join.

Whichever faction you are most in the green with is your faction.

There is also a mod called MP Neutrality or something that allows you to start neutral with everyone when you being a MP game.

ok, but say you have reached the limit of animosity from a faction, does that still work? I was in a bar and talked to a corsair rep who told me he couldn't help me in the least, and that if I don't leave something bad would happen... see, I don't want to kill the enemies of a faction and piss off the whole world only to find out that nothing I do will save the relationship to begin with.

or maybe I should call dr laura on this one?

I was totally hostile with Corsairs.

Don't take missions to kill their enemies (Red Hessians, outcasts, mollys) but just explore and shoot them.

A few hours mining in Dublin and shooting Mollys brough my Corsair Faction from hostile to neutral. Some more time spent exploring and destroying Red Hessians got it right in the middle. Docked with a Corsair base and took one mission which brought me up to Friendly status.