You are wrong about the Boy Scouts. I was a cub scout and a boy scout and have seen the indoctrination towards accepting christianity and rejecting any other concept. The camping and skills were interesting but the preaching was stifling. I already lived in wilderness camping, hunting and fishing on my own so I quit just before the transition to Eagle Scout where the indoctrination was even more intense. Scouting was more about accepting authority than learning personal skills and values.
As an Assistant Scoutmaster, I have to call BS on some of what you said. The BSA at the national level has their joining requirements for youth and adults that you can consider the minimum joining requirements. Local councils grant a charter to a chartering organization which could be anything from a school to a church to the local VFW or Masonic Lodge, etc. These chartering organizations can have additional joining requirements. For instance, a Catholic church can charter a Pack or Troop and restrict membership to their church members or to only Catholics. A school can limit their membership to only their students. A charter grants an organization to use the scouting program as part of their overall outreach in the community. So, the church that charters a Scout Troop can say that the Troop must have a worship service on the Sunday morning of a campout and that it must be a Christian evangelical service. Most troops I know are chartered by churches, but they are open troops and the church does not restrict membership or dictate program. A few do.
Any youth or their parent can vote with their feet and shop the market. There are 11 districts in my council and 25 troops in my district which covers only a portion of Oklahoma City. If you don't like the way one troop operates in my district, you have 24 others to visit and join. In the metro area, there are probably at least another 50.
Religious indoctrination in scouting is determined by the chartering organization pure and simple and most don't go in that direction. My troop has been chartered by a United Methodist church for the last 45 years. We have white, black, asian and hispanic kids. Most are evangelical Christians, but we do have Catholics, a Jew and a Muslim. Our "services" when wee have them are about 5 minutes in length and totally non-sectarian. They are put together by the boys and not adults. When we say grace, we simply say amen at the end instead of "in Jesus name".
Scouting has nothing to do with accepting authority. The mission of the BSA is, "The mission of the Boy Scouts of America is to prepare young people to make ethical and moral choices over their lifetimes by instilling in them the values of the Scout Oath and Law." The vision of the BSA is, "The Boy Scouts of America will prepare every eligible youth in America to become a responsible, participating citizen and leader who is guided by the Scout Oath and Law." This is done using the patrol method in the outdoors. We teach boys how to become independent and leaders, not to "accept authority".
And you don't transition to Eagle. You earn it. Only about 5% of Scouts ever attain the Eagle rank.