What was the conflict between Miss Maudie and Mrs. Merriweather?

I would add to the first answer that another reason for
the conflict is Mrs. Merriweather's reference to Atticus helping Tom Robinson; it is
clear that she does not approve of it.  After she complains to the other women that
"some people" think they're doing the right thing by defending Tom, Miss Maudie snaps,
and I paraphrase here: "His food doesn't stick going down, does
it?"

This is Maudie's way of showing her disapproval of
Mrs. Merriweather's absurd, racist remarks, and especially her attempt to criticize
Atticus (while eating his food!)