What do you mean by progressive Muslims? I feel like in Shia Islam there is no movement towards living like a Salafi or being archaic for example, so wouldn’t that make all of us “progressive”? As in we exist in modern society, use technology, work etc.
Maybe some Muslims are more traditional where for females they wear Abaya and don’t work, and the men support the household but I don’t know many of these people who are my age.
If you mean people who are politically liberal then I think the inclination to left wing politics comes from being grouped into categories and being “othered” in society similar to LGBTQ people. I’m not saying this is right or wrong but I see why it happens in western societies.