The organization began allowing gay youth in 2013 and ended a blanket ban on gay adult leaders in 2015. In 2017, it made the historic announcement that girls would be accepted as Cub Scouts as of 2018 and into the flagship Boy Scout program — renamed Scouts BSA — in 2019.
I can’t speak to the Mormon exodus. That was before my time. But yes, they’ve gone through a lot of reforms from what I’ve heard from the long-timers; and from all of the training (e.g., YPT, two-deep leadership, etc) I had to do.