I think you might over-estimate how common that would be if such hate and opinions were not supported by the state or at least not ignored by the state, but it is an understandable concern, but I see a few possible arguments against it.
the lack of such freedom of mobility and movement of culture would let cultures mix and have more interaction, which has been shown to increase acceptance of different cultures, and reduce hate.
there will almost always be cultural differences, and dislike between groups, but especially without class struggles it will be less common for them to elevate to the levels of lynchings, and outright conflict. Hell, even just looking at the US, it has a decent amount of separate cultural regions but not much conflict based on that. It is mostly interpersonal conflict, class-based, or from reactionaries to minorities.
I think you might over-estimate how common that would be if such hate and opinions were not supported by the state or at least not ignored by the state, but it is an understandable concern, but I see a few possible arguments against it.
the lack of such freedom of mobility and movement of culture would let cultures mix and have more interaction, which has been shown to increase acceptance of different cultures, and reduce hate.
there will almost always be cultural differences, and dislike between groups, but especially without class struggles it will be less common for them to elevate to the levels of lynchings, and outright conflict. Hell, even just looking at the US, it has a decent amount of separate cultural regions but not much conflict based on that. It is mostly interpersonal conflict, class-based, or from reactionaries to minorities.