As a counterpoint, I don't know of any friends or close acquaintances who would consider feminism or femininity a dirty word. To me, it's a fairly straightforward proposition:
Q: Are you pro- women having equal rights to men w.r.t. social structures, family responsibilities, economic opportunities, etc.?
A: Yes?
Q: And are you willing to take a second look at your social and professional conduct to make sure it doesn't put your female peers in difficult, awkward or uncomfortable positions?
A: Sure, why wouldn't I.
Hooray! you might be a feminist, it's not that hard.
Also, personally don't see what's wrong with unisex products, and I think it may be possible companies might possibly occasionally find the odd not-shitty cause they can back because their employees collectively believe in the positive message and that also aligns well with their goals, and not solely because of a small group of cynical PR managers running focus groups.