Don’t be fooled by the superficially amicable split between the Boy Scouts of America and The Church of Jesus Christ of Latter-day Saints. The breakup, in fact, reflects a long-festering period of incompatibility and will have consequences for both institutions and for the possibility of respectful disagreements in our federal republic.

The immediate impetus for the divorce might seem to be the decision by the Boy Scouts to rename itself “Scouts BSA” in recognition of the fact that girls may now participate in its activities. This development, however, is just part of the evolution of Scouting, the most American of institutions, to reflect contemporary values of inclusion along the lines of sex, gender and sexuality.

As late as 2000, the Boy Scouts won from the U.S. Supreme Court the right to exclude openly gay Scout leaders. But as the gay-rights movement advanced, the Scouts’ position softened. In 2015, just after the Supreme Court’s landmark gay-marriage decision, Obergefell v. Hodges, the Scouts officially ended this ban. The opening to girls, announced last year, similarly expresses the gradual weakening of gender binarism.

From the perspective of the LDS Church, all this change was unwelcome. The Mormon church spent a century developing a close, even symbiotic relationship with Scouting eventually it was mandatory for all boys. For Mormons, participation in the archetypally American social practice of Scouting was a marker of full belonging in American social life.

At the same time, Scouting was a manageable symbol of cultural assimilation, because the Scouts allowed Mormon boys to belong to troops that were predominantly or exclusively Mormon. Because Scouting embraces religious values in the abstract, this model worked well for both sides. Eventually, Mormons seemed to compose as much as a fifth of all Boy Scouts.

After the opening to gay Scout leaders, the two sides attempted to negotiate a settlement in the form of institutional federalism. Although no national policy prohibited gay Scout leaders, Mormon troops could effectively choose their own leadership, which in practice would not include openly gay people.

The first important lesson of the split is that this experiment in private federalism failed. In the end, federal solutions work when both sides have more to gain than to lose by staying together, and when both sides display the creative capacity to reimagine what it means to belong and share values. Now, it would seem, one or both elements in that equation have changed.

For the Scouts, the moral is that changing to meet newly emerging social and legal norms has real-world costs. You can’t make a social justice omelet without breaking some traditionalist eggs. Yet Scouting was correct to allow gay leaders and to open itself to girls. Had it not done so, the institution would have relegated itself to a slow process of becoming a cultural backwater, not the stand-in for commonly held cultural values that it aspires to be.

For the church, the lesson is more subtle. On the one hand, by eschewing the Boy Scouts, the church is turning in on itself, rejecting one of the most powerful symbols of its hard-won mainstream American character. On the other hand, that the church is prepared to do so signals its justified confidence that the LDS Church is now so thoroughly accepted as American that it can afford to give up the symbol of Scouting.

In a sense, this double-edged sword captures the fascinating and challenging dilemma for the church. Its influence and legitimacy have never been greater. Yet certain strands of its social conservatism risk a gradual process of remarginalization. It will take decades for this existential situation to play itself out. The Scouting divorce will become a key chapter in the history of contemporary Mormonism.

The last lesson is for those of us, neither Scouts nor Mormons, who still want to believe in the possibility of respectful civic cooperation in a society that seems increasingly divided along religious and cultural lines. It was comforting to look at the mature, thoughtful, careful efforts of the Scouts and the LDS Church to try to resolve their differences. That two famously polite, helpful, kind organizations with so much in common could not make their marriage work doesn’t say anything good for the rest of us.

Our federal union, itself the product of compromise, is designed to allow for disagreements to alternate with shared commitments. To do that, we need to be broad-minded in culture as well as politics. The Scouting news is a reminder that it isn’t going to be easy.