Feminism is not a monolith, nor is it a dogma. The only thing you have to believe in order to call yourself a feminist is that ensuring women's freedom and equality of opportunity in all spheres of life is a crucial priority. That's it.
Feminists all work from that basic axiom, but aside from that we are an incredibly diverse group. We are diverse in five ways:
1) We come from every conceivable background and life experience. There are feminists from every country, every socio-economic class, every religion, every sexual orientation, every profession, every race and ethnicity.
2) We are diverse in terms of style and personality and lifestyle.
3) We are diverse in terms of emphasis. Some of us focus on fostering equality in the realm of sex. Some of us are concerned with the equality of opportunity for professional women. Some of us care most about cultural attitudes regarding the proper roles and characteristics of men and women. Some of us criticize organized religion, while others work for reform from inside faiths such as Catholicism or Mormonism or Islam. Some of us stress the issue of violence upon women. Some of us are primarily concerned with reproductive rights. Some of us point to gender apartheid in places like Saudi Arabia, while others criticize inequities in comparably more "liberated" societies in the West.
4) We are diverse in terms of the conclusions we draw from our feminism. Feminists often disagree with each other on all sorts of things. For example (and this is a gross simplification, by the way) some feminists believe that pornography is inherently degrading to women whereas others may believe that participation in pornography is potentially empowering. The point is that both camps are looking at the issue in terms of how pornography affects women's freedom and equality. Both camps are feminist even though they reach diametrically opposed conclusions. As another example, I believe strongly in the equality of opportunity for women in business, but I would be very much opposed to the United States imposing a quota like Norway's where companies are legally required to have a 40% female board of directors.
5) We also have other things we care about that aren't about feminism. My husband is one of those maddening people who will say, "I don't think I'm a feminist. I'm a humanist because I am not ONLY concerned about women's equality." But I haven't met too many feminists who are concerned about women's equality and nothing else. For me, I care very deeply about ending the death penalty, ending the corporal punishment of children, protecting our civil liberties across the board, and ensuring equal treatment for men, gays, people with disabilities, people of different races, etc. etc. etc. among many other issues that are not specifically feminist.
I suppose people may be inclined to say that my definition of feminism is so broad as to render feminism irrelevant. People often ask, well, doesn't everyone think that women should be free and equal? Sadly, the answer is no. There are whole nations devoted to a system of crushing gender apartheid. And in our own culture -- remarkable though our progress has been over the last three or four decades -- limiting assumptions about women's proper role run rampant and highly influential organizations like Focus on the Family are doing what they can to turn the clock back for women. I try to illustrate what I see as the continuing relevance of feminism issue-by-issue in the posts I write, but I have also alluded to that contining relevance here and here.
For me being a feminist means starting with the basic axiom of feminism -- that ensuring women's freedom and equality of opportunity in all spheres of life is a crucial priority-- and then coming to my own conclusions on each feminist issue.