Idk how old your kids are, but if/when they’re old enough to have a conversation with nuance, just talk with them about the myth of the Lost Cause. Maybe watch some Checkmate Lincolnites videos on YouTube to help. This applies to all sorts of topics of discussion, by the way. Have a fact-based conversation once they are ready, and land on your opinions and show that you arrived there based on the facts as you understand them, encouraging them to take the same sort of approach to any nuanced conflict. In this way, you can still enjoy the music you like without necessarily condoning the message. But keep in mind that unless you’re pirating that music, you’re still financially supporting the artist, so do with that information what you will.
If they aren’t ready for such a complex discussion, you can still make it clear that you like the guitars, drums, etc but not the lyrics, and you can say that the song is about people being mean to people who don’t deserve it and tease that you can talk about it more when they get a little older.
Idk if it’s relevant to you at all, but I rediscovered the Southerner album by Trent Dabbs recently and it’s pretty solid if you want something a little country-ish without being so problematic. Paper Trail in particular is a fucking vibe.