Of course you don't. Instead, you create something new that is responsive to Biblical principles, as the Scouts used to be.
I speak here as a former Scout, local council executive officer and Eagle dad. Thankfully, my son earned his award before the national organization accepted perversion.
Right now, I wouldn't recommend Scouting to a boy. We didn't allow our daughter to join the Girl Scouts for the same reason. Let's create youth organizations that truly honor God instead of simply offering lip service.
If you remain, you will be under the boot of a corrupt organization that answers to sodomy, inc.
I think I would counsel using a different organization for the boys under my care but at the same time retaining one’s membership in the BSA. The objective would be to keep that organization in contant turmoil, so it cannot be presented as some sterling program for boys.
IOW, I’d keep the wrecking ball operating within that organization. I’d want it to look unwholesome.
And, in the same way as the left always does, some conservatives should be sleepers in the hierarchy awaiting the day when they are in a position to steal the show back.