So now that we can identify as anything, is cultural appropriation no longer a thing?

There is a world of difference between cultural appropriation and reverence for a cultural tradition. If you really identify with another culture, you are very likely to respect the elements you are adopting. And most cultures will readily embrace that.

If you are making light of cultural elements, mocking them, or adopting them without understanding the deeper cultural underpinnings, then you are not really identifying as part of that culture you are playing with it.