I think it’s OK to keep eating your favorite foods and talking with an accent, especially if it’s your natural speech, as in, you’d have to re-educate to get rid of that twang. As to being “proud” of something. Do you have to brag about it to enjoy it?
Culture is a lot more than the Five F’s (food, fashion, festivals, flags, famous people). I think every culture has its problematic aspects and we can discard those with care. That takes work. Not everyone in the culture will agree with you. But you are as much a representative of that culture as they are.
Cultures also have myths. Every culture has them. They tell us who we are, essentially, as members of that culture. Nonconforming members of a culture have always had to re-define themselves and their cultures of origins, re-discover new threads that will allow them a greater measure of acceptance.
At this point, everyone who’s not actually from the South has now equated all of Southern culture with the single word “racism”. There’s a push to take away all the beloved myths of the White South (the gallant “lost cause”) and replace those stories with… nothing. This is a big mistake, but those myths can’t be foisted on people by outsiders. Someone from within that culture has to create a new image of a “New South” that focuses on those aspects, and historical figures, who resisted the norms or who were representative of something other than those norms.
There are already multiple Southern cultures. Nobody says that Black Southerners are “racist” or that their culture is “racist”, or that they’re racist for just existing. In this New South vision I’m throwing out there… what is the vision for including, or relating, to all the people who live in an area?
So the “New South” could include liberals who are very Southern in their accent, their food, but who are absolutely committed to progressive values… and who also have thought out for themselves how to express those values, they’re not just taking direction from carpetbaggers and know-it-alls from other states.
You can also choose the values that you want to embody and uphold in your personal conduct. You can extend those values and apply them in a more inclusive way. Southern hospitality extended to all, Southern good manners without the hypocrisy, whatever seems “Southern” that you really are proud of. You don’t have to brag, just embody the trait. And be honest about your family past, know the facts. You don’t have to broadcast those facts unless it’s important in the context of something else.
OP mentioned antebellum architecture. Can’t “embody” that. I like it, too, but can’t really imagine myself living on one of those plantation mansions, can’t even imagine re-purposing one of those buildings into anything other than a museum. I wouldn’t get married in one, or host a party there, because they are such a powerful status symbol of the past.