The previous answer was very strong. I might want to add that the notion of men not liking the work might be better framed as being disdainful of the novel, as much as being challenged with a new frame of reference. What makes the work so much of a force to the traditionalist notions of narratives is that it asserts and advocates for the voices of women. The female narrative structure helps to provide voice where there was silence and helps to create a new voice in the discourse. This is a challenge to any particular structure, and the forceful and clear nature in which Walker's work resonates in the conversation of narrative and identity might be a reason why there was such an intense reaction to it on the part of men. It might not have been dislike as much as being introduced to a new voice, which is always a process where there is reticence and hesitation. Over time, if the narrative is emphasized and underscored with greater regularity, it becomes an established voice in the diaspora of thought. This might be proven with the work, itself. Walker's themes and characterizations of men would not be seen in the same light of "shock" and "dislike" now as they were when they were first introduced.
I do not know the basis of your statement about men not liking The Color Purple, but I would not be particularly surprised to find out some men did and do not. The way men are portrayed in the book is not particularly flattering. We have a father who is sexually and otherwise abusive and a woman who turns away from men to love women. Men are generally not as "good" as women in the novel. Was Alice Walker saying that all men are terrible? Certainly not, but she created male characters who were terrible. To the degree that men feel that a fictional male is somehow a reflection on all males, there probably was and is some unhappiness about the book. When a woman is portrayed quite negatively in a book or movie, women often feel the same way. I remember when the book and movie Disclosure appeared, authored by Michael Crichton. The male employee is sexually harassed by his female boss, and she is a dreadful character. Women who read the book and/or saw the movie were not pleased!