Hello, schrafinator.
I don't believe that "feminism" is simply the belief that women and men should be equal. It seems to me that it is so obvious that women and men should be equal (although I do recognize there are people who disagree with this) that this would be too trivial a definition. I would think that a reasonable definition of "feminism" (and any other "-isms") should also include an understanding of the nature of the barriers to equality, and maybe the actions required to remove or overcome these barriers, and hopefully that it is but part of a greater movement to ensure equality and dignity to all people.
My idea of feminism has always included the recognition that:
(1) Women and men tend to have stereotyped expectations and positions in society;
(2) These expectations tend to demean women and squelch their fullfillment as human beings (this is also true for men, too, although to a much lesser extent);
(3) The barriers to the complete fullfillment of women are structural and cultural, being based on deep seated beliefs taught from childhood and reinforced by society's institutions; and
(4) The removal of these barriers will require a deep resructuring of society.
I don't know much about NOW, and I can accept correction on this matter. My impression is that the organization doesn't push enough to created the deep changes in society needed to ensure equality of the sexes. In my opinion, true equality is simply not possible in a capitalistic, materialistic, imperialistic culture such as the U.S., or even Europe. My impression is that NOW has the naive program of trying to promote a society much like contemporary middle-class America, except that women and men are equal.
American society is based very deeply on the oppression of minorities at home and the imperialistic subjugation of peoples abroad. So even if women could be equal to men in a society very similar to contemporary America, this would simply be allowing women to take their "rightful place" among the oppressors.
On the other hand, by insisting on equality, and working hard to promote equality, and by examining the progress and identifying the barriers that still remain, it may be possible, by incremental changes in the quality of women's lives, to actually effect the necessary structural changes, even if that isn't the intention at the time. But I would think that a conscious awareness of this would be part of the definition of feminism.