Women who don't believe in feminism believe in feminism. They may not like the label but their attitudes reflect it anyway. Same with many men. Anyway, it all depends on how you define it, but short of some political nutbags in the GOP, most people support some form of belief in equality between genders.
I was around at the beginning. I bought into it completely. Eventually, either I just became aware or perhaps the movement changed. I became aware the movement was to empower women to have choices. Thing is, it's turned into empowering women to have choices, but it needs to be the choices they "deem" to be the choices.
Which variety of feminism? The one that insists that women are superior. Not me. If you mean the one that says woman are basically the equal of men and should have equal rights, I believe in that one. Men and women are different from one another in more ways than sex, but it's only differences, not superiority/inferiority.