It's not a piece of real estate.
If most of the people playing it are Asian and female, it becomes their music as much as anybody else's.
I should have been clearer. I should have said: Classical music is a product of white/western culture, and no amount of finagling and redefining composers and periods is going to change that.
So far, whites have not had a problem with people from other cultures learning and performing classical music. All this talk about “cultural appropriation” might drive some folks to change their mind about that.