That's simple, right? Men and women, we are equal. Anything else associated with feminism- control over fertility, criticism of media treatment, concerns about representation in power structures- flows from that simple, defining belief.
Determining whether or not you are a feminist or whether an organization is inherently feminist, is equally simple. Do you promote actions or ideas that treat women and men equally? Does the organization act in a way that results in women and men being treated equally?
If not, neither you nor the organization are feminist. You may wish to be a feminist, but if you don't hold to that belief, you are not. Go find another word. This is not to say that feminism is a monolith and that all feminists believe all the same things. I've heard equally good arguments for and against pornography and sex work from feminists I admire equally. I've heard some fairly silly arguments regarding subjects like wearing colours and skirts* from feminists I otherwise admire. However, even those arguments are within the framework of equality for all sexes**.
For example, is the Catholic Church feminist? The short answer is "no, what the hell is wrong with you?", but you probably didn't stop by for the short answer, and I'm stumped on what happens next in my book, so I'll ramble on a bit.
If you're not familiar with the Catholic Church (hereinafter "RCC"), even a cursory examination of the structure and teachings of the RCC is enough to show it is inherently misogynistic. Men rule the RCC. From priest to cardinal to bishop to pope, the entire power structure is exclusively male. Only men can lead worship services, only men can make policy decisions, only men speak for God. Women have two roles, and both those roles are in service to men: wife/mother and nun.
This is not feminism.
The policies of the RCC flow directly from this misogyny. Women are not allowed control over their bodies, and are fully expected to die in difficult pregnancies and to bear the child of their rapist, even if that rapist is their father, even if they are 9 years old. Women are fully expected to give up any possibility of a career and to bear one child after another until they no longer can. That is the role of women in the RCC and it will never change, because the policy makers will never be women.
This is not feminism.
Having established that, is it possible for a Catholic to be feminist, or for a feminist to be Catholic in good standing holding to the accepted teachings of the RCC? No. Logically, one could not embrace the above and be a feminist, simply because the beliefs of the RCC and feminism are mutually exclusive.
Now here's the thing about feminism: feminism does not promise you a rose garden. Even if feminism overcame all misogyny tomorrow, that doesn't mean every individual woman's life would automatically be perfect. Feminism seeks to remove artificial societal barriers keeping women lesser than men. Feminism does not require that each woman become a doctor or limit herself to two children or abort her rapist's baby. Feminism merely seeks to make those choices available to you. You are more than welcome to choose to be a stay at home mother, to have eleven children and to continue any pregnancy you wish, even if that means risking your own life in the process. I would not make those choices, personally, but I'm not you and I will support your right to make choices, even if I might personally find them bizarre or ill advised.
Basically, in the linked article above (and here, why make you scroll?) Simcha Fisher argues that because she takes advantage of certain advances earned by feminists, she is a feminist. Just soak that in for a minute.
What if I had to argue with the auto parts clerk to buy a headlight bulb, even though I was the one replacing it? What if the bank required me to get my husband’s permission for this and that? And what if I wore skirts because I’d be shunned if I didn’t, and not because I felt like wearing them?
So what makes me a feminist? Some would say that all faithful Catholics are feminists, because the Church is the most pro-woman organization around: The Church honors and values the particular gifts of women, and demands that men treat women with dignity and even a little bit of fear. John Paul II famously called himself a “feminist pope”; and in practical terms, the Church has probably done more for the physical well-being of women around the world than any other charitable organization.
Catholics who are feminists recognize that, while so many true wrongs have been righted in the last 50 years, the poor treatment of women in America has just been displaced, not eradicated. So now, instead of corsets and disenfranchisement, we have widespread pornography, abortion, and abandonment of every kind. We have gained some necessary ground, but lost so much else that is valuable in the process. Most of my Catholic friends see the world this way.
*Admittedly, I wear skirts almost exclusively because I find them to be significantly more comfortable than pants, so maybe I just don't want to hear a feminist argument against skirts. Then again, I'm in favor of men having the option of wearing skirts (you'd think, given the, um, dangly nature of male genitals, that skirts would be the automatic male preference) as well, so I think I'm still falling within the equality test.
**We need to have a discussion about how limiting and exclusionary it is to discuss sex as if it is only male and female. There are those who fall outside the XX/XY paradigm, and it's hurtful to them to be constantly excluded from, quite literally, everything.