You're conflating capital punishment of convicted criminals by public hanging with the extra-judicial lynching of Blacks in the South. You're also dredging up American history from the 1600, 1700 and 1800's when people were executed by being hung in the town square.
You're attempting to link those hangings or lynchings to what happened in the South before 1964 and the Civil Rights Act. Public hanging and lynching share similarities and both have the same effect, death. Many public hangings of Blacks happened in the South as did private lynchings sometimes by mobs and sometimes by just a couple of people that used their hatred to take the law into their own hands.
A lynching is nothing more than an extra-judicial execution, usually committed by a mob. Hanging was but one of the possible execution methods utilized, dependent upon the mob's sadism. The "crime" (guilt usually not proven) could be anything from mistaken identity, mere suspicion, being related to another "criminal" or suspect, being "uppity", looking at a white woman or looking a white man directly in the eye all the way to theft and murder. Sometime after 1880 lynching (the victim) fell most heavily upon Blacks than Whites. Sadly the phenomenon happened in all regions of the U.S., but the Southeast, Southwest (Texas and Oklahoma), and parts of the Midwest seemed to have the most occurrences.
2018 reached the centennial anniversary of the lynching of Mary Turner in Valdosta, Georgia. To get an idea of where the mentally of the South still resides in it's deepest darkest recesses, just read the story about Mary Turner. The memorial marker erected to her was shot several times the first year it was erected in 2010 and since then has had many more bullet holes shot into it. So if you believe that the comments of Cindy Hyde-Smith had no darker meaning than a judicial hanging of a convicted criminal, I would suggest you give that a second thought.
"A Hundred Years After Her Lynching, Mary Turner’s Memorial Remains a Battleground
The Ways We Remember, Forget, and Erase the History of This Tragedy Is an Inescapable Part of Its Story"
A Hundred Years After Her Lynching, Mary Turner's Memorial Remains a Battleground | Essay | Zócalo Public Square