I don't want cultures separated by species. I want cultures to be culture-specific. For instance, Agrarian communities who value hard labor and simple life and deep connections with their community are not only going to be halflings and humans. Every person who feels connected to that kind of life, will be welcome based on their individual temperament and fit for the community.
Most of the civilized realms in my games are not "human-majority" or even "racial-majority" cities. Humanoids of all kinds gather based on economic or social preference, or are stuck there based on circumstance. Species groupings are more likely to be seen in neighborhoods and smaller, familial communities within larger communities. Humans are not the overwhelmingly most populous species in the world. It's pretty much a diaspora of many species (the new world was settled 250 years prior by a diaspora of refugees from a dying world.)
I agree the culture is the organizing principle. The languages that one speaks are one of the most powerful shapers of identity.
I assume many ancient communities were founded by a particular species. But over time, especially the large cities tend to become metropolises, multicultural and multispecies. Traditional communities can survive, whose founding species remains the majority. For example, the Halfling river nomad culture seems Halfling-majority even while other species are present as citizens and family members. I view the remote Grugach communities as founded by Elf and Orc working together to succeed in the harsh environment. There can be a magocratic culture that comprises mainly Human, Elf, Gnome, and Giant, in about equal numbers, whence also multispecies mixing them.
I tend to use the term "-majority" to emphasize, even a community known for a particular species will also include members of other species.
Factions seem a useful mechanic to describe social movements within a culture, including prestigious ones or criminal ones. Depending on the formal ideology of a faction, its members can be "typically" its alignment. For a combat game like D&D, factions are the place to find the "good guys" and the "bad guys", or similar combat motives.
Descriptions of a wider culture benefit from ethnographic neutrality. Possibly, the format and mechanics can also help ensure a culturally sensitive description. Rather than stereotype the behavior of an entire culture, I find it more helpful to list which backgrounds are prominent, while making sure to diversify this list.
There are conflictive sensitivities. There can be a distinctive cultural identity whose members strive to transmit to future generations, such as that of an Indigenous culture. Oppositely, there can be metropolitan culture that freely intermingles cultures around the planet. As long as each community has a reasonable process to "adopt" a stranger who wants to be part of it, it seems ethical enough to me.