The grandmother in this story is definitely a racist, as she believes that white people are above black people. She uses racial slurs like "pickaninny" and "nigger," which are words that demean the people of color that they are used to describe.
The grandmother does not seem to harbor any ill-will or malice towards black people, but she certainly does hold herself above them and believe that they lack the intelligence and refinement of someone like her, an educated white lady. She calls a little black boy on the side of the road "cute" at the same time that she uses a racial slur, and she does not seem to understand how offensive the slur is. This shows that it is not hatred that she feels towards black people but, rather, condescension, as of someone superior acknowledging the existence of someone inferior. She goes on to say that people like the little boy "don't have things like we do," showing us that she even has some sympathy for the child, perhaps, though she views him as being beneath her socially as well as economically.
She again employs a racial slur when she tells a story about a gentleman who used to bring her a watermelon every Saturday and how he dropped the melon off one day with his initials, E. A. T., carved into it. Apparently, a young black child ate it because he thought it said "EAT." Once again, there is no malice in her tone, but she implies that the child was idiotic, and they all laugh as a result. In some ways, she is a product of the era in which she grew up, but we can still identify her as a racist.