Hi all! I am not the most skilled athlete but I would like to pursue more athletics at boarding school. Which schools offer thirds teams or JV teams with fewer/no cuts for those who are less experienced? and which schools are more “accepting” of the mediocre athlete? Thanks 
Most have thirds or freshman teams, and quite a few also have developmental teams. Often, it depends on the sport.
A quick look through the schools’ websites will answer your question. As mentioned above, it depends upon the sport; more popular sports will have thirds, often, while fringe sports will not.
Depending on the school and the sport, you might not need much skill to make a team. Most of thesr schools are quite small but field a lot of teams.
Look at the athletic sections of the school websites. It is easy to find which sports have thirds teams. Also some schools offer personal fitness or other options for less sporty kids. Some schools will allow a term off, or to substitute theater or arts for a term or two as well. You can ask questions about this when you visit the schools.
Kids who are not athletic type joins these teams. My all three kids at BS loved their third teams, and made many lifelong friends
Just about every boarding school I know has thirds teams or the equivalent. Most of these schools require students to participate in afternoon activities, commonly competitive sports, so they have to make a place for the less skilled athletes.