They may be sworn enemies. But that doesn't matter when it comes to your soulmate. When you find that other half of your heart, when you find the one who matches you in every way, you can't help but fall in love. And I love that in the end, what brought them together wasn't magic but rather their own choices.
And reading the Kyoshi novels really puts that into perspective. Korra didn’t ruin Aang’s characterisation. It simply revealed the nature of the Avatar cycle. Even Yangchen created problems for the avatar that came after her.