is definitely a sexist movie. Although the film's major thesis is the emptiness of modern culture, with its focus on consumerism and social isolation, unfortunately it also squarely correlates the rise of the strong independent woman with the emasculation of men as the cause.
In the beginning of the movie, the Marla character is the evil/self reliant/independent/ emasculating woman, showing up at all kinds of places she doesn't belong (i.e. men only support groups)-- demanding, by her very presence, equal access to a man's world, and by so doing, destroying Jack's feeble attempts at control. Once Jack has his psychotic break, empowered by the overtly misogynist Tyler part of his personality, he can begin to put women in their rightful place (according to the sexist framework), by diminishing her to a plaything (a sport fuck), and excluding her from the "club" (men only, even if they have bitch tits). Finally as the movie reaches resolution, Jack rejects the misogynist and violent attitude towards Marla, and instead takes on a more paternalistic role. He saves Marla from her suicide attempt, and puts her on a bus (for her own protection).
But this paternalistic relationship to women is just as sexist. Marla is reduced from being an intellectual threat in the beginning of the movie (an equal in the game), to an infantilized subordinate in the end -- the movie ends with Jack putting his arm around Marla, who looks up at him in bewilderment, telling her everything is going to be alright...