...in four paragraphs:
Libertarian: I mistrust government, a whole lot. I believe that market forces are preferable to legislation when it comes to getting things done, because they are more voluntary (consent is always best) and more easily reversible. I believe that the pursuit of happiness is a personal thing and takes different forms for different people, and the government's main job should be to allow us room to conduct our individual pursuits. It should prevent us trampling on each other in the process and enable those of us who by circumstances of birth or misfortune have been denied the ability, but otherwise stay the hell out of the way. I am a left-libertarian, not a paleoconservative, states' rights, or Ayn-Rand-worshiping libertarian.
Feminist: Sexism is a bigotry that generally takes the form of explicit assertion or implicit suggestion that men must be one thing and women another, and that women exist for men (as ornamentation or care-givers, means of reproduction, and so on) rather than for themselves. I oppose any attempt to institutionalize this idea via law, and argue against the endorsement of it in culture. I am an individualist feminist, not a difference feminist or misandrist.
Atheist: I consider it highly unlikely that our great big messy very old universe came into being via the deliberate machinations of an infinite mind, much less the kind usually asserted to be responsible for doing so. And if the complexity of this universe, and of us specifically, requires explanation by appeal to such agency, then surely the agency itself demands such all the more. I believe that supernatural beings are neither required nor sufficient to supply existence with meaning or morality. I am a "good without gods" atheist, not a "believers are stupid" or "believers are evil" atheist.
Skeptic: Science is a tool for knowing the empirical world-- the best one we have. Considering that, it would be a shame not to use it whenever possible and when we do forget to use it, it's always to our detriment. I view mystery as a door to open and explore beyond rather than to hammer shut with nails marked cultural reverence, tradition, religion, or magic. I believe reality is always more fascinating than the myths we make up to replace it, but imagination is important because it's our ability to wrap our minds around what is really real. I am a "let's find out the truth" skeptic, not a cynic, pessimist, or "You must share my other ideologies or else you're not really a skeptic" skeptic.
Note: This post brought to you by two discussions I've read recently in which at least two of the above were alleged to be incompatible. I am convinced that they are not, or at least don't need to be.