Foot washing is found in the New Testament book of John. Before He is betrayed and crucified, Jesus ended his final meal with his disciples by pouring water into a basin and washing their feet. This was an important act in Jesus's time and setting: wearing sandals in a dusty climate meant that feet got very dirty while traveling from place to place. When he had finished, Jesus instructed his disciples to use Him as an example; in his absence, they should wash each other's feet because "no servant is greater than his master, nor is a messenger greater than the one who sent him" (John 13:16).
In theory, a "foot-washing Baptist" would describe a person who interpreted this act literally, performing acts of service with great humility to serve mankind. That's not how Mrs. Maudie uses the term, though. She tells Scout that some of the local Baptists did not find her gardening to be in accordance with their views. They believed that she enjoyed taking care of her flowers so much that it was sinful. According to their views, she should spend more of her time indoors reading her Bible and less time gardening. Miss Maudie continues by telling Scout that these "foot-washing" Baptists think that she (and Scout) are examples of walking sin because they are women. This is a reference to Genesis, when Eve is accounted as the source of original sin when she disobeyed God in the Garden of Eden.
"Foot-washers" are so caught up in following the "laws" of the Bible that they often miss the big picture: Christians, including Baptists, are called to love their neighbor as much as they love themselves. People like those who would condemn Miss Maudie for gardening believe themselves to be more "religious" because they adhere to a strict code of laws, but they miss the calling of Christ when they condemn those around them. Just as Christ served his disciples with a humble spirit, Christians should love others and serve them with a genuine spirit, not one of condemnation. This is the point Mrs. Maudie is trying to impress upon Scout.