It's my own program, but I would say UT Southwestern qualifies. The main clinical site is a "safety net" county hospital system that mostly serves non-insured/Medicaid folks, many are not English speaking, and most receive what is effectively free care. We also have an affiliation with the community mental health system for Dallas and surrounding counties and do rotations there (essentially the same population as the above but for mental health). Advocacy is a relatively prominent part of the culture and the residency program leadership encourage involvement at the local, state, and national level. We have residents that do non-clinical rotations with a Texas policy think-tank based in the Dallas area, and one of our residents gave a keynote address at the NAMI Texas conference last year.
All that being said, I think issues like policy advocacy and social justice issues are things that will need to be driven by you more so than the program. There will be plenty of opportunities to explore this interest if you make it a priority.