The Empire is legally rascist; there's a widespread belief that Sith blood (carried exclusively, pretty much, by pureblood Sith and mixed-blood humans) is the source of their force abilities, a belief supported by the fact that everybody who has the whole redskin thing going on is force sensitive at least.
It's also complete BS, since the founders of the Sith Empire were human Dark Jedi conquistadors, with the conquered Sith as their slaves.
The Republic race relations are a lot more like the modern US, where human racial supremacy was the law of the land for thousands of years when the Pius Dea movement controlled the Republic. And while Pius Dea and its Crusades haven't been government policy for millenia, humans are still the upper crust of an astonishing amount of the galaxy, their language is probably the most widely spoken, and their probable homeworld is the capital of the Republic.
A whole lot of folks (human and non) regard humans as the norm, an idea that tends to get support since there are races, such as the Chiss and Miraluka, which actually are offshoots of humanity. And then there's the fact that humans are, if not a majority, certainly a plurality of the known galaxy's inhabitants.