I think it becomes obvious as you read the novel that segregation occurs across all levels of society, not just among the black community between the whites. For example, it is clear that the Ewells occupy a lesser position on the social scale than others. Social status is evident in Maycomb just as it is in all societies.
I love To Kill a Mockingbird because it breaks all the barriers and stereotypes at the same time it highlights them. For example, all the poor people are not the same; consider the difference between the Cunninghams and the Ewells. Nor are all white people the same; consider the cantankerous Mrs. Dubose and the gossipy Miss Stephanie. Also consider that some whites exhibit extreme prejudice while others defend Tom Robinson from injustice. In the same way, not all blacks are accepting of whites. When the Finch kids go to Calpurnia's church, most are welcoming, at least in deference to their father. Lulu, on the other hand, is aggressive and clearly thinks these white children do not belong among this body of believers. She is beautifully escorted away, but her attitude is absolute proof that racism goes both ways in this novel.
If you are asking whether only black people have prejudice or dislike aimed at them, then clearly the answer is no. Clearly, black people feel some animosity towards whites and want them to stay in their "place" too.
We see this from the fact that Jem and Scout are challenged as they near the church. Calpurnia is scolded for bringing the white kids to the black church. Most of the black people at the church do not feel that way (or do not express it) but there is at least some support (among blacks) for the idea that blacks and whites should remain separate.