Is there a stigma associated with LPS, and are LPS students allowed to join fraternities?

I saw a similar post on reddit, and was curious. From what I’ve read on different threads on here LPS students are free to join any club or organization they choose, however they’re not allowed to play Varsity sports. A few reddit posters said they didn’t think LPS students could join frats, but I’ve also seen cc posters mention LPS students joining frats at Penn.