Chaney and Sanchez studied responses to gender-inclusive bathrooms; best practices for designing these sorts of rest rooms have been receiving a lot of attention recently, for example here: https://qz.com/933704/how-to-design-transgender-friendly-bathrooms-that-make-people-of-all-genders-feel-safe/. Chaney/Sanchez report that “While gender-inclusive bathrooms serve a practical function of providing a safe public restroom for transgender individuals, they may also signal identity safety [in other words, fairness] for women and racial minorities who may experience identity threat in organizations. . . . we demonstrated that women . . . and racial minorities (Blacks, Latinos; . . .) report greater procedural fairness [i.e., less discrimination] and a more positive gender . . . or racial . . . climate in organizations with gender-inclusive bathrooms compared to traditional bathrooms. Further, these effects were due to . . . gender-inclusive bathrooms. . . signaling more egalitarian social environments.”
Kimberly Chaney and Diana Sanchez. “Gender-Inclusive Bathrooms Signal Fairness Across Identity Dimensions.” Social Psychological and Personality Science, in press.