The topic of intersectionality is important in this case because all of the participants in the conversation are members of some minority or disadvantaged group. Allen is homosexual, Robert is African-American, Henry is Hispanic and Shirley is a woman. When it comes to gender identity and preference, Robert and Henry would be considered to hold more power. However, when it comes to race, Allen and Shirley are more likely to do so. Moreover, Henry and Robert are from a lower socio-economic class.
Intersectionality addresses how different racial, social, political and gender identities overlap, and what this means for people's interactions. As a consultant, you would have to discuss how this perception influences the relations of power that exist among the members. You should also address how sexist behaviour is handled in the formal and informal bureaucracy. For example, through the use of dialogue, sanctions, workshops or penalties.
The most important thing to address is that all perceptions in this case are valid, as the power relations are real and they overlap in complex ways. However, it would be important to remind all the participants that the workplace is meant to be a safe space for everyone, and therefore, the bottom line is that respect and professionalism should be present in all interactions, regardless of the specific characteristics of each participant.