Such an organization or person is pluralistic, or "culturally pluralistic" if you want to avoid any confusion with other meanings of pluralism (e.g. the political theory).
I nod approvingly in the direction of multicultural, which has all the trappings of a buzzword in current usage. However, I prefer pluralistic because it indicates not merely a tolerance of disparate cultures but a belief in their ability to coexist amicably without losing or sacrificing their unique identities.
Where multicultural is an obligation in modern society, pluralistic is an aspiration. Where multicultural signifies tolerance, pluralistic signifies integration without assimilation.
Consequently, I think it serves better as a counterpoint to xenophobia, without reaching as far as xenophile.