I’ve never been involved in BSA or Trail Life, but it depends on how well the child is equipped to handle loss.
The grim reality of spiritual warfare is that it will cost you other worldly achievements, and how much a child can handle that reality is really up to the parents’ discretion. The Eagle Scout designation carries a certain amount of prestige and indicates that the individual has trained to survive in the wild. The problem is, the spiritual battle aspect can mean that a Christian can train for years in the Scouts to try and get that award, and then the spiritual battles can make it so they don’t get it. Or worse, they get it and never accept the Gospel. Or they accept the Gospel, but then Eagle Scout has come to mean something anti-Christian, and so the Christian Eagle Scout has to distance themselves from that. I understand why they founded the other organization - Trail Life is just Christian and doesn’t have all of that complicated baggage.
Now if a child knows that the values espoused by the Boy Scouts are incorrect and wants to join that organization anyway as a witness to others, I would allow them to do so. But I would tell them their witness for Christ comes first, and not to get attached to any of the achievements they can earn, because they are likely to be kicked out for their faith.