In a more common setting, I'd make xexnophobia less prevalent than Eberron. Mostly because those settings are more "point of light" to take a 4th edition reference. I don't think either racism or xenophobia as we know them could develop as a widespread sentiment in early medieval France or England, when nearly everyone spent his whole life within 20 miles of his birthplace. Imagining racism requires knowledge that different people exist, and I am not sure it was the case, except maybe in very general terms. Imagining xenophobia require a sense of "nationalism" that was probably not in the mind of most people before the 19th century.
I think you're conflating nationalism and xenophobia in an ahistorical way. There's no doubt nationalism promotes a peculiar form of xenophobia, but xenophobia is ancient, and if we're looking at a rural, local society which barely knows about other places, there will likely be generalized xenophobia towards outsiders. This is even reflected in D&D's source material - the hobbits of the Shire are quite clearly xenophobic of and suspicious/doubtful towards "outsiders". This isn't the same as "racism", note, and even seems to apply to hobbits to some extent. They even have patrols going around looking for outsiders who might be "causing trouble". And the xenophobia/suspicion doesn't easily go away, either - not even for the nicest of good people.
So I think vague xenophobia and suspicion are reasonable, but race-specific stuff tends to be excessive, and one needs to be wary of making NPCs have unpleasant personalities, especially most NPCs, as some DMs do.
The fact that the races are different means that there's going to be racial prejudice, stereotypes, and assumptions.
You're conflating a bunch of stuff together here.
Racism, xenophobia, bigotry, and racial stereotypes. These are related concepts, but they're not the same things. Racism, as we understand it, tends to be pretty organised and the ideas widespread and typically very negative and often entrenched. Racial stereotypes aren't always negative, and are prejudicial, but not necessarily in an entrenched or hostile way ("Elves talk like this!" "Hobbits love food!" etc.). Xenophobia is a fear of the different, and is typically pretty common, but not the same as racism. Bigotry can be on almost any basis. So just having stereotypes doesn't mean you have racism in a meaningful way, especially if they're not entrenched.
I've played in a number of campaigns and settings where races didn't fit their typical then-stereotypes, note. Taladas (1989), is a great example, with barbaric Elven raiders, depressive non-thieve-y Kender, competent and brave Gnomes, Minotaurs who lead a great and organised empire, Dwarves who feared the underground, and so on. And it was well-put-together enough that it didn't even feel like it attempted to counter obvious tropes. Only when you simplify it like I am does it seem that way - otherwise it just tends to make sense from the history and context of the setting.