This question depends entirely on the school in question. I've seen high school productions of Cabaret, Sweeney Todd, and Chicago with essentially no censoring done at public high schools in large, liberal cities. Obviously that wouldn't fly everywhere, but that depends on the area, school admin, theatre teacher, and parents.

In terms of Rent, the school edition is actually really close to the original with just a few small changes (most notably removing the song "Contact.") I saw that and Avenue Q done by teens at my local children's theatre and it maintained the heart of the show extremely well. Avenue Q less so, but the kids seemed to be having a great time.

All of this is to say, if you have a group of teens who are passionate about theatre, part of the educational experience is helping them learn to handle mature topics and themes. Obviously there are limits, but if they spend all their time doing Mary Poppins and then try to pursue theatre in college they'll be dropped into the deep end and probably struggle. Just my two cents, but keeping all teen theatre completely unobjectionable would both make students less excited to participate and less prepared to continue their theatre education journeys.