Racial, ethnic, and gender minorities face mental health disparities. While mental health care can help, minoritized groups could face discriminatory barriers in accessing it. Discrimination may be particularly pronounced in mental health care because providers have more discretion over accepting patients. Research documents discrimination broadly, including in access to health care, but there is limited empirical research on discrimination in access to mental health care. We provide the first experimental evidence, from a correspondence audit field experiment ("simulated patients" study), of the extent to which transgender and non-binary people, African Americans, and Hispanics face discrimination in access to mental health care appointments. We find significant discrimination against transgender or non-binary African Americans and Hispanics. We do not find evidence of discrimination against White transgender and non-binary prospective patients. We are mostly inconclusive as to if cisgender African Americans or Hispanics face discrimination, except we find evidence of discrimination against cisgender African American women.