Watch some early episodes of Hawaii 5-0 from the 60s. They constantly had Asian characters played by non-Asian Hollywood actors. Both Montalban and Mark Lenard played Japanese with fake eyelids.
On the other hand, I gather that since the show was actually shot in Hawaii, they did feature a fair number of actual Asian or Pacific Islander actors, certainly more than most shows of the era.
On Mission: Impossible
, they only ever did one episode set in an Asian country, specifically Japan. On the plus side, all the Japanese guest characters were played by Asian (if not necessarily Japanese) actors. But on the minus side, the story expected us to believe that Leonard Nimoy wearing fake epicanthic folds could fool actual Japanese people into thinking he was Japanese. There were earlier episodes where Rollin Hand or Paris impersonated Asians with unconvincing makeup, but at least they were only trying to fool Westerners, which is slightly more plausible.