Should government insist that all private organizations comply with its own sense of the good?
No, overly broad comment not allowing a reply. There are various complexities involved here and "good" is just too open-ended anyway. Racial discrimination or rules over environmental protection are both a form of "good." There are also concerns related to let's say cafeteria employees versus students/academic personnel or things like health insurance needs. I would allow wiggle room and some local discretion but "it depends."