How does gender change the effect of "Everyday Use"? As a culture, do we respond differently to males and females who leave their family to seek their own way? Why or why not?

Generally, I would say that it depends on the context in which people "seek their own way." In the cases of both men and women, some of our perceptions about life choices are, more often than we realize, based on prevalent gender norms. There is a pervasive tendency, for instance, to think that women and girls are more attached to family and are more oriented toward the goal of marrying and having children, though this is less true than in the past. Arguably, in the past, many women adopted this goal less out of personal interest than out of a need to cater to social pressures.
In "Everyday Use," the family's response to Dee is based not only on gender, but also on her being a black woman who had the courage to make a place for herself in the world and to learn all of the things that she wanted to know. The fault with Dee is that she uses her education, as well as her trendy interest in the black consciousness movement, for vainglorious purposes. She forgets that the purpose of the movement was the uplift of all black people. She uses her education, which would not have been possible without the efforts of the community she left behind ("we raised the money, the church and me, to send her to Augusta to school"), to assert her superiority. 
As readers, it is possible that gender bias might make some of us less tolerant of Dee than we would be if she were a male character. She is flashy, vain, selfish, tactless, and demonstrates a remarkable lack of compassion for her sister. However, what is brilliant about Walker's story is that Dee's behavior would be equally egregious if demonstrated by a man or by someone who is not black. Her behavior toward her family undermines the very cause that she professes to support. Her supposed connection to heritage—even going so far as to change her name—draws her no closer to those from whom she is actually descended.