I don't know if this will be of any help in your research.
There may be some Rankin people still living in McNairy Co., TN. When I lived there one was the president of a local bank. I left there in 1995. With the name Rankin being not a great distance from Marshall Co., MS., the Rankin and Abernathy families you are researching may have moved together.
More on Abernathy. There was an M. R. Abernathy, (I think the M. stood for Matthew) who went to McNairy Co. in the mid 1800s from Alabama. He was a school teacher.