Where are you seeing "Equality, South Carolina"? in what source?
I did find that there was a post office for Equality and was shown on J.H. Von Hasseln's Map of Anderson County, South Carolina. Anderson, South Carolina, 1897.
You can see that map here (but good luck in finding that post office! :) )https://www.loc.gov/resource/g3913a.la000833/
Update: You can select "Mapping Services" after you search for Equality at the USGS and it will pinpoint where Equality was. Looks like today it would be at Hamlin Rd and Old Greenville Highway.