My question is: If you want to be on a certain college’s team, do you have to be enrolled in that specific college? For example, if I wanted to go to one college for a specific major that does not have the sport I want, can I join another college’s team?
Most likely, no.
it depends on possible reciprocal agreements the two schools might have. For instance, one young lady I know attends an art college in Detroit. Since the art college has no sports, their students are allowed to join club and ncaa teams at nearby Wayne State University through some sort of agreement. She was a top notch HS cheerleader and got permission to be on the WSU cheer team.
Pretty sure Bryn Mawr students can play on Haverford teams if Bryn Mawr does not offer the sport (likewise with Barnard and Columbia, but I think that’s expected).
For varsity teams and especially for NCAA sports, I believe this is generally only allowed in specific cases, such as some of the Claremont Colleges that have joint teams. In general I don’t believe it’s allowed though.
I think things can be looser for club teams.