I think this mostly works with the current order of the world, but it would also mean that e.g. a white supremacist in japan is left wing (since the current social hierarchy there if anything has japanese people above the rest - and please no one twist this into me saying japan is ultra racist).

It seems more to me that a common thread for anything considered "left" is that there should be no or very little social hierarchy, whereas right wing ideologies think there should be a very strong one (be that inherently through circumstances of your birth or merit based). In reality most places do have quite a bit of social hierarchy (and used to have more) so it coincides with wanting to change the status quo.

There's probably something I'm forgetting that is considered left wing and loves hierarchies