Race does affect Hurston's life, but not all times or in all ways. In her essay, "How It Feels to be Colored Me," we see that the times race affects her are those times when the behavior of white people forces her to be aware of her race.
We learn that she did not know she was "colored" until she was thirteen years old. This is because she lived in a community surrounded by other people of her race, with limited exposure to white people. She had no reason to think about race at all during this period of her life. She says,"White people differed from colored to me only in that they rode through town and never lived there" (para. 4). So, while she registered that there was a difference, this difference had nothing to do with race.
A change came when Hurston was sent to school in Jacksonville at age 13. We can infer that she was now entering a world in which there were white people with whom she had to interact, perhaps teachers and classmates and certainly townspeople. Since Hurston was born in 1891, this would have been about 1904, a time in the south in which overt racism was rampant, a time in which Jim Crow laws were in effect, subjecting African-Americans to discrimination that was perfectly legal. She is no longer "Nora," but "a little colored girl" (para. 5). Her realization that she had a race at all is not a good one, since she is not perceived as being a particular person, but perceived only a person of a particular race. What a troubling loss of identity this has to be!
But Hurson rallies from this loss, saying that she refuses to be "tragically colored"(para. 6). In spite of the persistence of people in reminding her that her ancestors were slaves, she goes about her life, able to be Nora, rather than just colored.
Nevertheless, there continue to be circumstances in which race as a construct affects her. When she attends Barnard, which was an overwhelmingly white college at that time, she has a great awareness of being in the minority. When white people visit African-American jazz clubs, she says, and she sits "in the drafty basement that is The New World Cabaret with a white person, my color comes" (para. 11).
So, yes, race affects Hurston, but not in all times and places, only when other people's attitudes and behavior call attention to race at all. And even with all of that, she is triumphantly herself, at the end of the essay, showing us a strong, proud woman who says she is not even angry about the discrimination around her. She says, "It merely astonishes me. How can any deny themselves the pleasure of my company?" (para. 16). She refuses to allow the limitations others place upon her to stop her.