I think so. But the key word there is majority. I think it might well be a majority, but I don't think it's anything like an overwhelming one (ie.. more like 60% than 99%). That still leaves an awful lot of people for who this organisation doesn't work particularly well.
Women's liberation over the 20th century also shows us that it's very much not a binary thing. Many modern women will embrace femininity when they're dressing up to go out, but also appreciate and take full advantage of the option to wear trousers and adopt more traditionally masculine attitudes when working of exercising.
As someone who doesn't have any inclination towards traditional gender roles, I somewhat question the idea that they are linked to our biological makeup. Or at least, I think it needs to be recognised that it is not as simple as men having one set of inclinations and women another. And I think it's quite important that society recognises this and gives people the flexibility to do as they want to not as their gender roles tell them they should do.