American multiculturalism up until WW2 was English, Scottish, Irish, French, Italian, Jewish and Greek. Strictly European, yet still featured plenty of discrimination within those tiers. The discrimination didn't end because people magically became more enlightened, it ended (or at least was greatly reduced) when the marginalized groups assimilated into a more homogenous "American" identity, which defaults to 'white'.
It's not clear where non-Europeans fall into this melting pot concept, because most are not racially ambiguous and cannot claim to be white. Most scripts will not have a protagonist of a specific race. But in casting, it will simply be assumed that the character in question is white. Because melting pot or not, that's what everybody's default is.