While being caucasian usually adds to the ''privileged'' stereotype, I think it's perfectly possible for a character of color to still be portrayed as privileged. In Kate's case, I've always read her privileged background as being mostly associated to the wealth and status her family has, and I think that could be translated into the MCU regardless of any ethnical background the Bishops have. I mean, it's no different than real life, really: POC do have some challenges for being POC, but if they're wealthy and famous, they do have privileges that a lot of other POC don't.
As for Aja, I've talked about this before, but I think he was actually the artist who made Kate look like an asian person the most, which I feel is partly where the fan desire for her to be asian comes from. So if they're taking inspiration from his visual work, I would be even less shocked to see asian Kate in the MCU.