What it comes down to is that the BSA is basically a franchise operation that offers its product to the various COs so they can suit their own needs in regards to youth outreach. Now obviously you can't mess around with the program too much after you start running it, a Big Mac still needs to be recognizable as a Big Mac right? So a Boy Scout still must be recognizable as a Boy Scout! But if they want to restrict membership or add new policy in a way that doesn't make them unrecognizable as Boy Scouts... Then they can! It's their branch of the franchise!
All that said every CO has their own aims and reasons for employing the Boy Scout program (or Cub Scout, or Venturing, etc!). If those aims and reasons aren't in line with the values and beliefs you want to impart on your child: I say have a frank chat with your son and look someplace else! Heck your current troop being hopefully Friendly, Courteous and Kind folk may even have some recommendations for you!
Anyhow it sounds like you're on the right track already and a lot of folks here have given you some solid advice! Good luck and good Scouting to you and your son!