According to the New York Post:

Oregon county issues face mask order that exempts non-white people

Lincoln County, Oregon, has exempted non-white people from a new order requiring that face coverings be worn in public

https://nypost.com/2020/06/23/oregon-county-issues-face-mask-order-exempting-non-white-people/

Does Oregon county actually have race-specific health orders?

(EDIT: Replaced "laws" with "orders" reflecting the verbage of the original claim.)