Can I, a Non-Native person, learn a Native language?

As the title says. For context, I am basically entirely white. My family says that we have ""indian heritage,"" but there's basically no evidence for this. Regardless, I live in East Tennessee on ancestral Cherokee territory, and would like to learn the Cherokee language, but I'm wondering whether or not it's *generally* accepted for a non-native person to learn a native language - though I'm willing to assume that there are probably some cases that differ from the consensus, whatever that may be. Thanks!

Edit: Thank you to those who've given me answers! And to the people who have asked why I ask in the first place, it's just because I've heard before that, for some, they feel uncomfortable having non-natives learn their language, and I figured I should ask just in case.