Honestly didn't know the etymology coming from an unhinged weirdo, but I've generally used it (irl mind you, I'm in China) as a handwaive when family asks about why X in the west is bad/inefficient/non-existent and "right wingers" isn't the cause.
Like what's with the aversion to nuclear power? Combination of 白左 and also the fossil fuel lobby.
Or if a policy that does (ostensibly) benefit poor people but is means tested to death, and they ask why it's set up like that. 白左
But I don't really often hear it in China. My family is just weirdly politically engaged due to being former Party members and revolutionaries. The average guy in the street is absolutely not going to use the phrase ever.
Yeah sure weirdos on XHS will also use it to refer to any aspect of the Western "left" they see online that they disagree with, but it's wholly inconsistent. Could be addressing Ultras. Or trots. Or liberals. Or redditors. Or nazbols. Or socdems. Or demsocs. I feel like XHS comment sections are like 2 steps away from calling Shanghai 白左.