Back when I was suppressing my trans identity, I was known as an angry person. Although basically mellow, I was perpetually dissatisfied and often verbally lashed out at anyone who slighted me. I often felt justified in my thoughts and words, even reveling in them.
But such a negative emotion gave little warmth to me. The glow of self-satisfaction of making cutting remarks quickly waned and then I was back alone, with my unhappiness and simmering anger.
No, chronic anger is not healthy. Physically, emotionally, socially.... it takes a toll. I think Veronique is correct that we shouldn't cooperate with oppression, but we do need to make peace with how we respond to it. A calm, clear-eyed focus on the big picture and the long term makes for more effective activism.
This isn't to say that we won't feel angry at times, or that we should never express anger - I think that, too, would also be unhealthy. But making friends with Anger and indulging it too freely is counter-productive, both in our individual lives and also in our social/political concerns.