That's not true. I've been asked that plenty of times by other white women. I've asked other women too, of all races. But only the ones I know or know to be generally working. And it's usually followed up with some nice sentiment about being able to let down for fucking once and have a day to oneself without having to take care of anybody.
Though I agree that asking women you're unfamiliar with is both loaded and problematic.
I've always been asked. In Alabama. In Orlando, West Palm Beach, Memphis, Tennessee, and out here in Arizona. I've lived a lot of different places and known a lot of different people. I've always been asked. Other white women I've known have been asked.
I'm not saying it has the same connotations to it. Usually it's more related to economic assumptions or whether or not you have small children. In fact, the only time frame where I wasn't asked if I work, with a time was when my Urchling was young. Then it was the opposite. It was "You work??" with a sneering what-kind-of-mother-are-you? tone to it. Mostly because those people knew I didn't have to. And I did cut back my working significantly. I didn't have a job. I did occasional gig work or temp work. Then started working part time when she was an older toddler.
People have always been weies about work. Ultimate point here is that it's not true that white women don't ask other white women if they work. And it is with a connotation of assuming they're out of pocket somehow....not doing what they should be doing. It doesn't have an attachment to slavery.