Historically connected to the people who fought to keep slaves. Neo-nazis are racist and think whites are superior. White guys holding up confederate flags at a white supremacist rally are racist nazis.
Yah, I don't entirely agree that holding a confederate flag means that you are a white supremacist. The south had slavery. During the civil war, the Confederacy did defend their right to have slaves, but they also wanted to defend their right to exist independently.
So when I see a confederate flag, it does demonstrate the desire for freedom and independence. So I do think that some of these people hold the flag with this connection in mind. It symbolizes the beginning of this country having a certain kind of freedom to start something new, etc.
The Confederate flag also doesn't exist because of white supremacy. It exists because, during the time of settlement and exploration, the north and the south existed more independently because of the absence of a system of communication that was eventually developed.
So the North had a flag of the first 13 colonies and the south had the confederate flag and a mail system began. The advancement of this early form of communication contributed to the civil war because otherwise, they would have no reason to know what the opposite side is doing and they would have no way to become unified.
So this advancement of communication produced a positive result and brought the end of slavery, but the history of how they lived distinctly at one point in time is fascinating and worth remembering and being proud of. Just because slavery existed in the south does not mean that people who feel a passionate connection to the history of the south are white supremacist and not simply people who strongly believe in preserving something that demonstrates independence to them.
There is also no historical connection between the Nazi's and the history of the Confederacy. Any connection that can be seen in modern times is created by fringe groups.