The most likely reason for the Boy Scouts’ policy is the belief that you can’t be a moral person without believing in God. As I explain in this article, such beliefs are widespread (shared by about 50% of Americans), but false. One can be an atheist and yet still have strong ethical commitments. And there is no evidence that atheists or agnostics have higher rates of criminal or unethical behavior than religious believers do.
It’s also worth noting that the Girl Scouts have allowed open atheists and agnostics to participate since the early 1990s, allowing members to omit the word “God” from the Girl Scout oath. There is no evidence that this has caused any problems for the organization. The Boy Scouts should follow their example.
There is absolutely no evidence that this completely speculative justification is the dominant motivation behind the BSA's exclusion of atheists. The real most likely reason for the BSA's policy is that it was founded by deists and liberal Protestants as part of the already somewhat deistic Scouting movement (it was often criticized as such at the time, although obviously from the other side); and at least some of those founders (West, most notably) were quite extraordinarily specific that part of their vision of Scouting was a society under God that included the cultivation of brotherhood among different religions. And the BSA has been more reluctant than GSUSA in giving that up as a key element is almost certainly due to the well-known fact that the BSA has always been much more institutionally conservative than the GSUSA, and that this is especially true in the past few decades, during which there has been an especially firm push within the organization to retain the basic elements of its glory days in the 1950s, to the extent that it can. The Boy Scouts of America have always been an active promoter of civil deism.
The founder of the modern Scouting movement, Robert Baden-Powell, was of course the son of Baden Powell, who was a mathematician and a very famous liberal theologian who argued against miracles and was an enthusiast for Lyell and Darwin. (The family changed its name from Powell to Baden-Powell after the good reverend's death.) Baden-Powell is somewhat coy about his own religious beliefs, but he was quite clear that his vision of Scouting included religious education. The religious education was very hands-off, in the sense that Baden-Powell is quite clear in Scouting for Boys that education in general is self-education, and that scoutmasters should apply this to religious education by encouraging boys to educate themselves in the subject and provide guidance as to where they can learn more, but to do very little more. (Amusingly, he sternly warns scoutmasters that trying to do more is likely to end up either boring the boy or "making him a prig".) So how is this self-education supposed to unfold? Baden-Powell connects it directly to two of the major elements of Scouting as he saw it: Nature Study and Knight Errantry. Scouting was in part to serve as a religious supplement to church -- whatever specific church it might be -- by giving boys a way to let their religious lives expand outside the church building so that it could directly link up with appreciation of nature (Nature Study) and active moral life (Knight Errantry, i.e., doing 'good turns'). Religion, like everything else, would be taught by the Scout method. Baden-Powell saw Scouting as a way of inculcating chivalry and nobility; just as the ideal knights of old would have had love of God and nation, so the Scouts, as a knighthood devoted to peace, would cultivate the same chivalry. The Scouting movement wasn't babysitting for boys; it was a civic education movement, based on the idea of brotherhood under God, for an Empire and Commonwealth.
It was an idea with a considerable amount of appeal, and, of course, it began to be imitated throughout the Empire. However, it also caught the imaginations of people elsewhere, and several different people in the United States tried to plant the seeds of the Scouting movement in the U.S. There's dispute even today over who was the first person to attempt to transplant the Scouting movement in the United States. Not everything was carried over -- American frontier in general played a bigger role than European knighthood, for instance. Likewise, these new organizations had varying relationships with the original Boy Scouts. But several of the people involved were especially impressed by the brotherhood-under-God idea. I've already mentioned James E. West, who was the first Executive Secretary of the Boy Scouts of America, and the one who is responsible for adding 'reverent' to the Scout Law. Boyce, the actual founder of the BSA, seems to have mostly been interested in 'making men', but he wasn't hugely influential in the actual shaping of the early organization. Many of those who were did not hesitate to advocate the importance of the brotherhood-under-God idea. West, as I said, was the major force behind this, although by no means the only one. One of West's early challenges was convincing Catholics that, despite the close links between the BSA and the YMCA, the BSA was not a secretly anti-Catholic organization. (We tend not to think of the YMCA as a religious organization, but there was a time when the 'C' meant something, and that was Christianity of a very Protestant sort. West's trouble convincing Catholics that BSA wasn't crypto-Protestant is somewhat ironic given that the KKK would later oppose the BSA as crypto-Catholic.) And he did a lot of work to put forward an American version of Baden-Powell's idea of Scouting as an educational movement that would include religious education without replacing that provided by churches.
One of the things that's very important to understand is that the Girl Scouts of the United States of America and the Boy Scouts of America are radically different organizations. The only things they have in common is that they are the most successful transplantings of Baden-Powell's original ideas onto American soil. The GSUSA was not the sister organization of the BSA. Actually, the sister organization for the Boy Scouts was the Camp Fire Girls, and it's arguably due to its long association with the BSA that Camp Fire is one of the few other original Scouting movements in the U.S. to survive the Scouting wars. The reason for it was that, while some Scouting organizations petered out, the BSA effectively destroyed most of the rest. West made it his mission to guarantee that the BSA was the American Scouting organization, the official one with the official ties to Baden-Powell's original Boy Scouts. It was his idea that there should be two organizations, Boy Scouts of America for boys and Camp Fire Girls for girls, and nothing else. Camp Fire Girls, of course, eventually became co-ed, but it even survived at all because it was the one non-BSA organization that the BSA did not go after. Other Scouting organizations were absorbed, pushed out, or sued for using the name 'Scout'. The Girl Scouts were no exception; West was out to get them. They survived only because they had powerful friends -- Juliette Low, the founder of GSUSA, had clear connections with Baden-Powell himself, so West couldn't pull strings there, and it later became difficult to attack the GSUSA when Lou Hoover, the First Lady, became its president. This is all to say that they are radically different organizations, with radically different histories, and radically different cultures; they share basic principles, having inherited a common set from Baden-Powell, but that and the name 'Scout' are about it. And historically the GSUSA has always been faster than the BSA at shifting with the times. There's a reason, for instance, that the Girl Scouts were more often praised by leaders of the civil rights movement than the Boy Scouts; the BSA was liberal enough in its attitude toward race that it constantly had problems with the KKK, but in practice it was quite hands-off on matters like segregation, whereas the Girl Scouts by the 60s had already actively begun to transition to a desegregated approach. Likewise, even though the BSA and the GSUSA share many common principles, historically the BSA has generally been more conservative in its interpretation of them.
So this difference is just of a piece with what has always been the difference between the BSA and the GSUSA. I think, though, that Smolin's claim, with regard to the GSUSA's allowing of Alternative Promises that atheists could use, that "There is no evidence that this has caused any problems for the organization," shows that he doesn't quite grasp the way the GSUSA works. It is in fact not true that there has been no damage; various Girl Scout troops, and parts of Girl Scout troops, splintered off specifically in response to the GSUSA's action in doing this. It's too early to say whether some of these splinterings are serious problems, although one of the splinter groups, American Heritage Girls, has been growing quickly enough that in a decade or two it may be a serious rival to the Girl Scouts in some parts of the country. Such things can be a pretty big issue; there's a reason West went after all rivals, and that was that keeping a toehold in a region requires a critical threshold of young people and resources flowing into the organization. And the GSUSA has never really fought large-scale territory wars the way the BSA has; it's just too early to tell how well the GSUSA would handle them -- if any of the splinter groups really take off (and, again, it's too early to tell if they will). These things take time, and it can't yet be ruled out that the GSUSA will take some serious blows for this. But the GSUSA is not run by stupid people, and they take their Scouting heritage quite seriously; they knew quite well what the danger was, did not go into it lightly, and after careful study and discussion decided that doing it was in accordance with the principles of Scouting as practiced by the GSUSA. The civil deism is still a big part of the organization -- it's just that they give options for people who don't accept that part in particular. But, again, they knew it would anger people, they took this into account, and after deliberation they went ahead and did it anyway. In doing so they were fully in accord with the principles of Scouting; Scouting has always been about educating for a particular vision of civil unity, and they came to the conclusion that, important as the 'duty to God' part was, it was only the default and not a necessary condition for that particular vision of civil unity promulgated by the organization. However, asking the BSA to act like the GSUSA is asking them to do something they probably cannot do. The GSUSA has only been able to make the changes it has because of the way it has grown up; they were able to make the changes in a way consistent with their traditional interpretation of Scouting and their cultural expectations for it. But the BSA has grown up a very different way, and it has completely different traditions of interpretation and a Scouting culture that is in a number of ways very different.
Which is not to say that it might not eventually make the change, of course; but my suspicion is that Smolin's advice that there would be no harm to the organization in making it would soon be seen to be facile -- my suspicion is that the BSA, which has always had to make an active effort to prevent and deal with splinter organizations, would be much more likely to splinter and break, and to do so much more rapidly, than the GSUSA. I think the move would be more widely resented, and local troops would be more likely to resist it actively, than in the GSUSA. And since the BSA is unlikely to suffer anything from not doing it, I rather suspect that the relatively slow-moving organization would never get around to making such a change in any case. But there are reasonably clear cultural and institutional reasons for this that have very little to do with any view about the particular relationship between morality and belief in God, even if the latter does serve as a contributing factor.