The word itself isn't the problem, and in general I don't have an issue donating to organizations that also tackle the problem on a political level.
With climate change specifically, if I can't reasonably rule out the risk that the org will spend the money to tell me that I can't have an air conditioner, meat, or travel (or worse, lobby my government to ban me from having these things), they're not getting any money.
I'm OK with taking some risk that the org will use money in a way that I consider non-optimal, but I draw the line where I see a risk that the money may be used directly against my own interests. "Don't feed the mouth that bites you", I guess.