As someone also in their mid 30s, I think a lot of people really misunderstand how the confederate flag was viewed so casually by many people up until recently. It was always offensive to some, but I genuinely was unaware of that as a teen growing up in the 2000s. It was just an image of being kind of edgy and rebellious but I genuinely didn't think much of it seeing any band using them. Watching Skynyrd or Guns N Roses videos of live concerts? There were "rebel flags" pretty often and I just kind of let it go. It meant nothing to me.
I was in my mid 20s, probably, when it really was explained to me how insensitive that can be. I never associated it with racism or slavery up until that point - and I'm pretty sure that's the same thought that a lot of these bands had. The absolute best thing to do is exactly as you said: own up to it, change your ways, and grow.
On one hand I am always amazed at what kids can learn and latch onto in the weirdest ways. So I have no doubt that a lot can be learned through context. Watching movies can absolutely demonstrate a seemingly endless scenarios in a way that can be understood.
However, as someone raising a child, let me tell you how often I have to stop and explain that certain things are not real just because there's a video of it. Or how many words are being used incorrectly because they were heard in one context that was misunderstood.
I think a child who only had media to teach them, with no one to correct things, would have an endless amount of misunderstandings - nevermind the amount of things they'd believe that are entirely fictional. Basically, no, this kid would be screwed.