Being that the movie takes place in 1938, how could it not be "how things used to be"
Although there were a few black jockeys in those days, they were not permitted to ride the best horses. I would guess that racetracks were segregated, too, as were most public accommodations in those days. Even basketball was a white man's game back then.
But this kind of whining from critics is ridiculous. As if every single movie about anything that happened before 1965 MUST either feature a black character, no matter how obscure or false, or else it must have a significant commentary about segregation, otherwise it is "hogwash." Sheesh. Can't we just enjoy a story about a horse without all this social-history crap getting thrown out?