I would say that since feminism is predominantly a political movement, it is precisely why many women wouldn't necessarily call themselves feminists. You don't have to explicitly align yourself with a political term to agree (or disagree) with certain ideas or viewpoints.
Many people would consider themselves to be left wing, will support things like worker's rights etc and might vote for Labour at elections, but most wouldn't feel the need to actually join the Labour party and attend the meetings and canvassing.
Many people are concerned about climate change, the environment and would support certain reforms, but most wouldn't join the Green Party or agree with their approach. Some might support the Greens, but decide it's better to vote Labour or Lib Dem during elections as they have a better chance of securing political power.
There was a website where you could read specific electoral policy from manifestos and agree or disagree with them. Turns out a lot of people agree with Green Party policies and principles without realising it.
So I think it depends on how your question is framed. "Would you call yourself a feminist?" might result in many women saying no for all sorts of reasons, including uninformed ones especially if they have heard negative connotations from media or friends.
If you start asking specific questions like "Do you think women should have the right to vote?", "Do you think employers should be able to discriminate against hiring women because of pregnancy?", "Do you think husbands should be prosecuted for raping their wives?" And so on. Then you might find that a lot of women will be in agreement with and supportive of 'feminist' ideas. There will be differences of opinions too, of course, but broad agreement of women's rights.
Even when women don't view themselves as feminists, it doesn't stop them from campaigning or protesting an issue, forming groups to address problems that affect them or finding creative ways to support other women.
And of course as mentioned by previous posters, there are various strands of feminism and differences in approach.
Some support equality of opportunity, others support equality of outcome, others prefer to focus on liberation instead of equality. So if you're going to consistently criticise 'feminism', you need to understand the differences first.
I most likely wouldn't be considered to be a 'good' feminist as I tend to be skeptical about certain assertions and disagree with certain approaches, but that doesn't stop me from being supportive of women's rights and issues overall. 