Poetry doesn’t have to be political, but it certainly can be and in many cases ought to be. Imagine, for example, trying to write an entire book of nature poems these days without evincing at least some awareness of the manifold threats facing the natural world. It would seem kind of irresponsible, wouldn’t it?
The problem though is there is so much truly awful political poetry – it’s almost as bad as love poetry for the surfeit of clichÃ©s and abstractions. I enjoy the challenge, and usually attempt to ground it either by making it very personal, as you suggest, or by using dramatic monologue. Sometimes it works.