Worst organization I've ever seen to do this is the United States Air Force.
Open prayer before staff meetings with the Base Commander (a General). The Air Force Academy openly pushes Christianity, and discriminates against non-christians.
Hobby Lobby, Chick-Filet, Boy Scouts of America - all have NOTHING on the USAF!
Domino's Pizza was founded by a conservative Catholic, and I stopped going there as soon as I heard of his public opposition to even the tiny liberal moves in the Church. He used, and may be still using, his considerable fortune to fund a conservative Roman Catholic community in Florida.
I'm a war veteran and won't join the American Legion partly because their slogan is For God and Country and makes no mention of serving veterans. The national organization has a long history of serving as enforcers for the federal government, as it did in the 1930s when it helped crush the WW1 Veterans Bonus March in Washington DC.
The national organization has long behaved badly toward the San Francisco post whose members are gay. By having their own post, its members are making a political statement by embarrassing national leaders.
I am a member of AMVETS and was a post finance officer for three years. I became inactive and a year or so later a post commander started opening and closing meetings with prayers. I protested to officers, telling them I'm an atheist and even telling them of the Matthew 6 verse that tells xians to go into closets and close the doors to pray. As do most xians, they cherry-pick their bible.
As most organizations do from time to time, this Post lost members and it's now barely surviving. I've been telling officers (and a man who fancies himself a chaplain in the posts of several veterans organizations) that praying encourages passivity when the post needs activity.
The post's members are all in their 70s or older (including me) and I keep in mind the words about groups that changes their practices as their older members die.
There's a wee bit of hope even for the Republican Party as its old white male members die.
Always an independent, I used to occasionally vote Republican, but stopped when Pres. Reagan invited evangelical xians to join the Party. No one had counted them and there were so many that they took over most state Republican parties.