I would say it would be wrong on several levels.
Firstly, you're duplicating expensive infrastructure for no reason. Why build separate but equal schools instead of building a school? Wasting taxpayer money for no apparent benefit is, in fact, a moral issue.
Secondarily but likely more importantly, you're going to increase disharmony. Consider that once you've opened the door to black and white options, you need to accommodate all the other races. So you need an Asian and Arab school now... but there are many subgroups there that don't get along so you really need a Japanese, Korean, Chinese, Kurd, Persian, etc. school. There will never be an end to it because no group will want to be lumped in with "and those other minor groups" rather than get their own school. Now add in the LGBTQ+ groups each wanting their own school, and notice how the number of letters has been steadily increasing over the years as more and more groups want their own distinctiveness. So now not only are you building dozens to hundreds of duplicate schools, you will face an ever-increasing pressure to build more and more group-specific schools.
Now of course you don't just need separate but equal schools, but all other infrastructure. Why share roads, voting booths, or anything else once you start on that road? A separate but equal military platoon isn't going to be happy with another race as their CO, we need complete separate but equal command chains so that doesn't happen!
This not only raises the actual cost to absurd levels, it increases disharmony because these various bits of infrastructure will never truly be equal. If you have separate but equal turnpikes, some race's turnpike is going to have to be the closest and thus shortest route compared to the others, and the same for every other option. Even for just schools, one school is going to be in an (at least perceived) better physical position and the schools can't share a specific block. Every inequity, imagined or real since some will be very real, will only raise ire and emphasize that X group doesn't really get all the benefits of Y group. Thus the level of social strife will increase from "Separate but equal."