let's take it further
What if, let's say, people in those stories lived together before marriage (or could date the way we can now), women had high-powered careers, or what if people back then could be openly gay, with no consequences to their social standing - no, still nothing? Still wouldn't take you out of the story because these are all good things and the way society should be anyway?
See, it's really not about race at all.
But this is essentially what you are saying - that they should have license to cast whoever simply because it's a good thing according to modern values. That is not the point, however.