i think it's slightly more complicated than that.

tighnari was one of the first sumeru characters revealed (and the first one released, along with collei, who's appearance has been known for years), so received the brunt of the frustration people had with the lack of skintone diversity.

dori's design has orientalist elements, so her pale skin made that worse. nahida had similar issues to tighnari, where she is the representative of the first region known to have a darker skinned portion of the population (rather than one off characters like xinyan and kaeya in liyue and mondstadt). faruzan's story is directly connected to king deshret, so people expected her to have desert blood.

whereas althaitham has been criticised for having an arab name and pale skin, and kaveh has been called "mondstadter"/had his origins questioned because of his blonde hair. i saw little criticism of layla, but honestly i haven't seen much discussion of layla in the first place.

it's just not as easy as "pretty privilege", especially in a game where everyone is designed to be appealing.