"Christian Right" and "Christian Left" are political terms. In both of them, "Christian" serves as a descriptive adjective modifying a noun. They're legitimate and useful terms, but although I am a Christian who takes an interest in politics, I can't identify with either one.
As a Christian who is libertarian (i.e., consistently in favor of individual liberty, both in economics and in people's personal lives), I think "Christian Right" tendencies toward theonomy or at least dominionism are dead wrong, and so are attempts to make non-Christians behave morally like Christians through legislation. I also think "Christian Left" tendencies toward pacifism and income redistribution, or at least high taxes and big government, are dead wrong.
Sorry, but I say a plague on both their houses. And I'll add that while individual Christians may be political, and good citizenship may even require it, churches should not be except on matters that unite all Christians. If any church aligns itself with either the Christian Right or the Christian Left, I won't be able to join it, and if they do so after I'm a member, I'll have to leave.