I ask because I can't recall hearing of anyone having any objections to Lucille Ball and Desi Arnaz, despite his being Cuban.
Prior to Hernandez v. Texas (1954) Mexicans and Latin Americans were seen as "white" insofar as the law was concerned. That didn't mean that they were free from discrimination as the culmination of Hernandez v. Texas stated unequivocally that Mexican Americans and others of Latin American descent were distinct and deserved protection under the 14th amendment. Though I'm mostly familiar with Texas, I'm not so sure how how that du jure status as "white" fared in places like the Deep South.