Well, Maryland did when I was there (though a quick google tells me they don’t anymore). Some of the public universities in California have their upper-division requirements structured such that even when it’s possible to get through without upper-division science or math courses, it’s not easy. It’s hard to tell for sure from the websites of the colleges my daughter’s looking at, but a number of the liberal-arts colleges seem to have such requirements, though they don’t always have complete lists of which courses fulfill which distribution requirements and they don’t always number courses in a way that makes their levels obvious anyway.
Interestingly, I also poked around and found only a very few few colleges that actually require upper-division humanities courses of STEM majors. Even at the one I teach at, where I’d thought there was such a requirement, it turns out that it’s only for selected majors (e.g., biology, math) but not for all (it’s not required for, e.g., engineering or health sciences majors).