Working with women

I love my job. One of the things I love about it is all the wonderful women I get to work with. Powerful women, docile women, energetic women...all varieties, all working together to prevent child abuse. It's incredible.
What I love, though, is also what I hate. There is always this game, this balance, of friend and coworker, supervisor and supervisee...and it seems someone is always offended at what another has said or done, or not said or done, or said in a different tone, or didn't use any tone at all...you get the idea. I feel like I'm constantly doing damage control; smoothing someone else's feathers, or my own. It can be exhausting. I think I'm joking around with someone, then find out they took offense. Someone is joking with me, and I take offense. It's ridiculous.
Today seemed to be exceptionally full of those games, and it left a bad taste in my mouth.
The tricky thing is, in order to bond on a certain level with people, you have to go outside a certain level of office formality. And once you cross that line, you risk falling into the cycle I just described. This seems to always happen, and I end up wishing I'd just stayed on the outskirts of the office friendships. Ugh. Maybe someday I'll figure this out.
I welcome your advice. Please.