Do politics exist in the Chain of Command? More specifically, do you believe soldiers that are "friends" with leaders get better treatment?

There are no "friends" in the CoC. I care about my Soldiers... every last one of them I would fight through the gates of hell for. That doesn't mean I hide their misdeeds or look the other way when they go off the reservation. Quite the opposite.
There are quite a few of them that once they leave my unit, I'd be happy to have a beer with. A couple that have become real friends after they retired or ETS'd. But I can't do that when we are all in the Army. It compromises good order and discipline, and while I hate to admit it, the impartial judgment I will need when the need arises.

This is a problem that not only pertains to the military but extends to corporate America and civilian life as well. I am usually not a well liked person in my chain of command because I refuse to take part in being friends with leadership outside of work. To further this, I also don't take part in career field traditions, and am not the typical person from my career field so I usually stand out as an outsider within the organization. You can say I'm the Batman of the Justice League =D

I am not necessarily hated, but the seldom "special treatment" I receive is usually earned rather than given.

It's just not politics but the good ole boy buddy system.