Actually, this was a territorial law, though it likely carried over to state law following statehood.  The "No Dogs or Natives Allowed" signs and similar were widespread, from what I've read.  My old friend Johnny Grames was highly respected by most who knew him.  His dad and uncle ran the Anchorage Grill, a popular spot in 1930s and 1940s Anchorage.  Their insistence of not allowing Natives into their establishment was one of the catalysts in spurring Gruening into action on this issue, though you hear little of that particular episode today.