Peer mentorship offers a promising strategy for promoting diversity, equity, inclusion, and belonging in physics. However, implementing a peer mentorship program in a predominantly white, male environment without critical insights can reinforce harmful narratives about who belongs in this field. Critical Race Theory provides a framework to prevent such harm by centering the experiences of students underrepresented in physics. This paper describes a large peer mentorship program providing academic and psychosocial support to undergraduates enrolled in physics classes at the Massachusetts Institute of Technology (MIT). Mentors were surveyed anonymously to understand their experiences as a function of ethnicity, race, gender, gender identity, and sexual orientation. The survey was designed to test the hypothesis that the mentor program creates a counterspace for marginalized group members where they feel a strong sense of belonging. We find that the mentor program fosters a greater sense of belonging than the mentors' home department. It creates a counterspace for marginalized group members in part by reducing the prevalence of harmful comments, actions, and behaviors within its community of practice. Three results stand out from the quantitative and qualitative analysis of the survey. Black mentors responding to our survey have the strongest sense of belonging in their major, possibly because they access other counterspaces supporting their academic success. Meanwhile, gender minority status, especially being non-binary or transgender, is the strongest predictor of a lack of belonging in our sample, and microaggressions are a key factor. Finally, faculty play a particularly strong role in fostering a sense of belonging or exclusion.