I can make some comments about Rice since my S25 is a freshman there this year (He visited Wash U and didn’t like it at all, but I didn’t go on that visit trip, so I can’t make any comparisons!).
With Rice, we definitely get the vibe that although there are many STEM kids (my kid is an applied math major), there are plenty of people studying other things as well. In terms of being able to live on campus all four years, the vibe we are getting is that while some students do get “bumped” off campus when they would have rather stayed on campus, the number is on the small side, at least in some residential colleges. In my kid’s Residential College, they haven’t “bumped” anyone in at least 3 years apparently - enough people chose to move off campus that everyone who wanted to stay could. There are ways students can improve their chances of getting to stay on campus by getting involved in leadership roles, committees, etc of their college.
My S25 is definitely meeting people outside his residential college. I would say for him it’s mostly people he is meeting through student organizations. In asking him who he hangs out with, he says it is pretty split between students from all over he knows from an organization he is getting pretty involved with, and friends from his college. He’s starting to get to know a bit people in his classes, but the one class he would really like to form a study group for has mostly students that are 2nd year or older (he thinks he might be the only freshman), so that’s been a challenge. But I’m sure as he settles into more major classes he will also be developing friendships there.