What does Atticus do to prevent his kids from catching the disease of Maycomb?

"Maycomb's disease" is racial prejudice. It's rife in the town, just as it was throughout the South as a whole. Atticus, however, is different in that regard, which allows him to represent Tom Robinson at his trial. It also allows him to raise Scout and Jem in the proper fashion, to inoculate them against the prevailing fever. One thing Atticus does is to teach his children the importance of putting themselves in other people's shoes. Although this applies to die-hard racists such as Bob Ewell, it also applies to the town's African-American population.
When Atticus mentions the phrase "Maycomb's disease" in Chapter 9, he's talking with Uncle Jack. Scout overhears their conversation. Atticus goes on to say that he hopes that his children will come to him and ask him if they have any questions concerning racial issues. This is a recognition by Atticus that there's a real danger of Scout and Jem picking up all kinds of prejudiced opinions at school and wherever else they go in town.
It's interesting that Atticus wants Scout to hear what he's saying to Jack without letting her know. After all, if Scout's going to pick up various scraps of racist talk around town, then it's important that she should hear counter-arguments at home. Given the circumstances of the time, this is arguably a much more effective method of inoculating the Finch children against the "Maycomb disease" than simply telling them outright that racial prejudice is wrong.