I run racism in Hyborea as very different than people expect but something that works very well for me. First, I show don't tell. Basically, everyone pretty much hates/holds in disdain almost everyone else. However, the tribalism of the people actually isn't that intense by comparison to much of the world.
Let's use a literary model for a start. Conan the Cimmerian
Conan the Cimmerian presumably reflects as much of Robert Howard's views on Hyborea as possible. Conan's racism is fairly well established. In the context of Howard, Conan holds the following beliefs.
* A sexual preferance for light skinned women (though not to the extent of excluding other women)
* A belief that the cannibal tribes of one region are loathesome (Howard's making of such a group is arguable)
And oddly enough, that's about it.
Strangely, while Howard might put in the Aquilonian sentiment that the Picts were not considered "white" by the settlers, it's noteworthy that Conan himself never expresses the view. He also has a nationalist distaste for a large number of kingdoms but more or less gets along with all of them.
It's very Edgar Rice Burroughs to have "The White Guy who can do everyone's Native Culture better than they can." However, Conan did that frequently with everyone's culture including most of the Whites. Conan out-Asgards, out-Aquilonians, out-Zamorans, everyone. Yet, also, Conan lived as a King of a Black Kingdoms tribe for goodness knows how long as well. He's not even prejudice against Stygians and gladly works for Set-worshipers when the money or sex looks good.
Overall, it seems that while racism was pervasive in Hyborea, it was also a very cosmopolitan culture as well. Conan the Cimmerian is able to get work in Aquilonia as a scout and pretty much every other place in the land. No one expresses any revulsion at Conan's many sexual congress acts with women of what we can only take to be a wide variety of races (even though plenty of women express horror at being captured by 'savages', they frequently do the same to Conan).
This is again, a very common form of racism around Howard's time but I think we should mark it's type.
Howard is probably around a 2 on a scale of 1/10 (0 being "Everybody is the Same") surprisingly and would probably count as reasonably progressive despite his Texas and conservative background.
Which I find surprises a lot of people but seems born about. Conan and, by proxy, Howard seemed to long to visit Exotic cultures and experience the world.