As far as to your first assertion of, "... if there's a war, the losing side doesn't get that kind of treatment." Then read more than what your state supplied history books tech my friend. I believe it there is a story of when the U.S. troops went through a city in WW1 I believe, possibly two but a civilian asked, "well what now? You mean to say you're gonna come blow up everything and then leave?! We arent now under your serfdom?"
"No!" he replied with a grin and continued his march.
"Well what of us then..? Are you not the americans?" meaning to imply this is and has been the norm up until this point.
The man chuckles and says, "it's because we ARE americans that I'm doing it." Meaning that we here, hold the idea of freedom to be worth dying for, for all if they so choose to do so.

Now with that established, on to your second paragraph. You asked what the, "southern way of life" meant to someone today other than slavery. As if that were the only thing notable of the southern states but yes, let's unpack this real quick:
1.) Now I understand that you may be offended by history because of what the prevailing ideas of that era were and for that, "waaaah... boo-hooo." Sob somewhere other than here because I sure dont see anyone going to any one of the countries numbered in the double digits and marching with these god damn signs... or the mass people attacking the ones, the first and ONLY ones who fought to end the practice altogether. That's... not smart, but if anything you might want to welcome whites with open arms for ending slavery as a trade instead of attacking them for it. Why? Let's be honest, POC feel that it's all about color but not all white people are the same. Look at the jewish community... not all whites are the same because they were the ones who owned the boats that transported the slaves, not ethnic europeans. No, they were the ones beyond sickened by the practice who sought to end the large number of their plantations in where? The antebellum south. That's righ, I said it. A small minority did not have slaves but instead themselves mostly ethnic slaves themselves. Now to be more direct on the reason for wanting the flag. In the original ideals of THIS COUNTRY our state's rules, laws, and representation, superseded the federal government power meaning like if now, CA wanted %100 amnesty for illegal immigrants then they would and COULD have it by that standard. The federal government had taken their stand against Great Britain, accrued a large debt as a result, so to finance the countries aftermath (which POC fought in willingly btw) there was to be an alliance, or collective body, of the colonies... of those, taxes were levied... and under the "protection" from GB by the government of the south opposed the collectivization of power to speak for the individual affairs of the south and as well each colony of the 13 original. So on many moral reasons o tree her than slavery, they opposed federal intervention in the affairs of the states.
"Its about heritage." you'll often hear them say. That means the heritage of the desire, that internal drive, to be free. To be free from oppression... all forms.... and you want to chastise that? Why? People should rally behind that because of the statement it makes to our government not because of the source of income the men had back then and other nations STILL HAVE TODAY. Again, I don't see these special interest groups protesting injustice in say, tel aviv for the african migrants there.. or over in juadong province against xi jinping and his tyranny. Nope...Only here in america, where that type of top/down oppression is ALREADY illegal. Only here in america where we are the ONLY country not under some form of serfdom already. (i.e. GreatBritain: the queen. China: political aristocracy and so on) So there's no glory, no issue and if it continues that key difference of us from them would be gone forever.
I'd start by asking who it was that owned the ships and are they still in slavery today? Caveat: it ain't white folks. and yes they are. They sometimes look white, that's all.