Even if it was mostly an obligatory formality, President Obama never let that on to the boys in the meeting. Despite overwhelming schedules, American presidents understood it was worth the time to hear some kids talk about Scouting’s opportunities for service and leadership. The stories from these meetings become legends among the generations of youth leaders, many of whom come back to serve as adult mentors in the program. President Bill Clinton, one of them told me, called each of the kids in the room by name after hearing their names just once.

Mr. Trump’s secretary of state, Rex Tillerson, happened to be an adult leader during my trip to the Oval Office. At the time, he was the president of the Boy Scouts’ executive board (a different position from the “honorary president” role now filled by Mr. Trump). The post was subsequently held by former Defense Secretary Robert Gates, who later endorsed the nomination of Mr. Tillerson for secretary of state in part because of their “mutual involvement in and leadership of the Boy Scouts of America,” according to a statement he released in December.

That involvement came at a time when the Boy Scouts of America was facing mounting pressure about its policies on gay members. The membership policy became national news in 2012, while Mr. Tillerson was the executive board’s president, and was changed in 2013. Under Mr. Gates’s guidance, the organization also changed its policy on gay scout leaders. Both men were closely involved in the process of moving the organization through these changes, and they saw firsthand the risks of getting mixed up in politics.

The protracted battle over Scouting’s gay membership policies owed much to the fact that Scouting in America truly cuts across all walks of life. There are troops in nearly every community across the country, and about 50 million living alumni. The Boy Scouts may skew toward its stereotype as white, middle-class and conservative, but it is a surprisingly diverse organization — of which its leadership is rightly proud — and Hispanics are among its fastest-growing demographic groups.