Lula does not want the white children in her black church because they are the children of Calpurnia’s employer, and do not belong there.
The interaction between Lula and Calpurnia is a perfect example of the racial tension in Maycomb. While the whites tried to keep blacks out of certain places, there were also places where only blacks generally went. First Purchase Church as the African-American church.
When Lula asks Calpurnia why the children are there, she responds that they are her company. Lula scoffs at this.
"Yeah, an' I reckon you's comp'ny at the Finch house durin' the week." (ch 12)
Lula has a point. Calpurnia and the Finch children are not equals. While Calpurnia loves and cares for the children, she is still hired help. Some of the servants are afraid the children will talk, seeing their servants outside of work. It is their private time, away from the inequities of racial tension.
Cal’s son, Zeebo, welcomes the children and tells them not to listen to Lula, because she has “got fancy ideas an' haughty ways” (ch 12).
In the end, the children remain at First Purchase Church for services. They see that most of the people there cannot read. However, as Calpurnia said, it’s the same God.