One of the interesting bits about capsuleer society is the inevitable contact with people of different races, creeds, nationalities, and ideals. Hatred, under those circumstances, is usually a challenge. Sure, you may encounter the odd raving fanatic, but you also run into the sane, reasonable, and thoughtful.
At that point, there are basically two paths. Either you start to see those you are coming in contact with as people more than targets, or you double down and determine that differences (such as slavery) are more important than how "nice" any given Amarrian might seem. That last is easier for the Minmatar than most-- it's pretty easy to cast largely-racialized slavery and programs of cultural annihilation in an utterly damning light.
On the other hand, Minnies are maybe the only faction that could do with fewer extremists. The Amarr/Minnie arguments on the IGS are utterly predictable and haven't changed substantially since at least 2006. All that changes is the backdrop-- do U'K hold space? Do the Amarr? Has Jamyl freed a bunch of people yet? None of it ultimately changes the discussion.
Of course, becoming more moderate need not change what you do very much. EM is less "out there" than U'K, but still fights the good fight against the Amarr.
One of Aria's favorite observations (cold-blooded little creature that she is) is that it is easy to kill people you don't really think of as people. It's much harder to look someone in the eye and say, "I recognize your humanity. I understand that you have been fighting for your own way of life, and your own way of seeing right and wrong. I can even think that we might have been friends, had things been different."
... and then shoot that person in the face.
I've always liked that as a roleplaying challenge. It's easy to be a fanatic. It's much harder to play a moderate who is still willing to kill for her beliefs.