I'm a Christian and a feminist. Membership in both groups is a key part of my identity. If you talk to someone with a simplistic understanding of these groups, though, they might be surprised that it's possible to be a member of both groups!
The problem is that we aren't very good at differentiating subgroups that happen to share the same label. We lump Catholics, Pentecostals, and Unitarians into one group called "Christians". We even lump Canadian Christians and American Christians into one group!
We do the same with feminism. Most people don't think about the various causes feminists support, and which ones they do support. Some feminists say men can't be feminists, others say men can and should (and here's another great article exploring that debate). Feminism had different "waves" of philosophy with their own unique characteristics: the first wave, second wave, and third wave.
I find it interesting that both groups (which I admit are usually opposed) suffer the same problem.
It all smacks of the No True Scotsman fallacy (video explanation, Wikipedia page). To borrow the Wikipedia example, the fallacy goes like this:
Person A: "No Scotsman puts sugar on his porridge."
Person B: "But my uncle Angus likes sugar with his porridge."
Person A: "Ah yes, but no true Scotsman puts sugar on his porridge."
I see this, or something just like it, all the freakin' time when having a discussion or debate about Christianity or feminism.
Devin: I'm a Christian.
Friend: What!? How can you believe in creationism? Obviously evolution is real...
Devin: I don't!! Of course I believe in evolution
Friend: No, Christians don't believe in evolution
Not all of the conversations are like this, but I've certainly had that exact conversation, word for word.
This isn't new to any Christian. The parallel to feminism is an interesting one though. It says something about huge social groups - at some point you can't define what someone is.
This probably extends to other large social groups in different domains, especially values-based ones. What is a Canadian? What is an environmentalist? What is a democrat, a conservative, or a liberal?
The solutions are simple and largely ineffectual: try to explain to people the subtle nuances of what you believe, rather than allowing the conversation to stop at the label. This means powering through the initial distaste someone might express if you tell them you're a member of a group they don't like (e.g. feminist, Christian, etc). It might even mean sidestepping the label in the first place, and instead pointing out the specific things you believe. For example, I specifically believe that I have a duty as a man to consciously listen to what women want more often than I'm normally inclined to. I also believe that God continues to work miracles in the world and I'll never understand that or be able to measure it.
But in the end, the only way we can increase understanding and tolerance is through patient and kind sharing of our ideas. Someday we'll get there, and I'm guessing it won't be in my lifetime. But it's still good work and there's no time like the present to get started on it.