Neutral lets ya get ships.

also how do you get to neutral

If ya want corsairs to like you, tear into red hessians.

(dresden system has a red hessian base that gets you lotsa kills)

For red hessians to like you, kill corsairs.

For all baddies to like you, kill bounty hunters.

In multiplayer, team up with someone who likes that faction, and have them take jobs FROM that faction. This is THE fastest and cheapest way to do it.

Try the freeports (they call them that for a reason) in the system or next to the system with a particular faction you want to get cozy with. Go to the bar and find someone to bribe to get your rep fixed up. If they are not there leave go to the equipment dealer or such and then go back to the bar until you find the right offer.

I would only do this method after the SP campaign is over as it is a waste of money otherwise (unless you need a particular item in a hurry).

Yes you can get neutral with all the houses some will still be a little toward the red side so be careful if you haul freight into those bases as you will get jumped and asked to drop your cargo.

Some prefer the slash and slay method of affecting your rep. Me personally I would rather buy my way out of it, as it is quicker and easier to me.

Just some thoughts from the edge of space!