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Step one would be to make sure that their overall program in terms of honoring Black History month, and black students, is in a good place to start with. As a private school in the US there is basically zero chance that this is true.
Step two would be to think about how honoring different food traditions works as part of menu planning in general. When you do theme ethnic lunches, are you actually respecting the traditions you're referencing, or just doing inaccurate pop-culture versions of cuisines to get easy "diversity"?
Step three would be to construct a menu that actually respected the history and experience of Black America through food instead of reaching for stereotypes. I don't think you'd see people upset about, for example, a weeklong menu that respectfully highlighted different black food traditions from America (soul food, Cajun or Creole, Afro-Carribean, Ethiopian, etc.) instead of just one thing that's easy to toss off without any real thought or understanding, both since that would include a bunch of different delicious foods and because it would highlight the diversity of the black experience in America.