@Beamur
I don't think that the left wing own feminism. Really really don't think it at the moment!
Feminism is also what you do and how you think, even if you reject the label. The label is name for it but it's still there whether you name it or not.
There are academic feminists, media feminists, career feminists (etc etc,) and there are those of us, most of us probably, just out there, being women, helping other women and pushing against stereotypes.
I don't think they do either. But a lot of them sure think they do.
It's really very disingenuous in my mind for people to suggest that's only some kind of online thing, and I'm not sure why that keeps getting repeated when people say that isn't what they are talking about.
Absolutely there are groups of women working for certain ends who don't bother with that stuff, they are interested in doing something about a problem - in my experience though it's fairly common for women in those groups to not call themselves feminists, or not describe their group as a feminist group. They are more likely to call it something like a women's group or focus on the specific issue.
But "feminist" groups - like a pp said, second wave feminism could be extremely exclusive and lots of more conservative women have felt literally pushed out of feminism over the years, it's been made clear the contribution of women like them wasn't wanted, they didn't fit in, they shouldn't try and contribute because they didn't believe the right thing about some subject.
The question in the OP and which people always ask is why do so many women not choose the label feminist. Well why should they when their experience is that they are treated as not good enough?
It really reminds me of what people and especially women complain bout with the LP - the feel like they are being told they own the LP, or feminism, their allegiance and numbers, just so long as they sit quietly and don't try and bring up their real views.
The don't get broad church allegiance because they don't present themselves as broad church. Maybe they shouldn't, but then the question is kind of "why doesn't everyone agree with me?"