The BSA had a policy of "leave it to the locals" around segregation by race during the civil rights movement. There was an explicit decision that admitting black scouts would "cost us many white boys" in communities where "grown people are willing to stand for lynchings of colored people." (Macleod) Putting it in context, black students were banned from the YMCA in Virginia and couldn't earn merit badges there, like swimming badges in the pool. The last segregated troop endured until 1974.

That said, the BSA did a lot to attract blacks into the organization. There was railway scouting, where a paid BSA organizer would ride the trains and dispense material to kids and parents at the stops. Black kids in the south were successfully attracted to scouting this way, with Memphis and Atlanta notable successes. And the BSA was aggressive in attracting blacks in Northern cities to the organization (with integrated troops widely available.)

The KKK was widely critical of the Boy Scouts as tools of the Catholic Church. Meetings could be broken up. There seemed to be a timidity to the Boy Scouts of America that they would adapt to local circumstances, even if that meant black troops couldn't wear uniforms in the south.

The Girl Scouts were a more significant force for change. They were founded by a suffragist who wanted to defy gender roles by teaching girls to pitch a tent. The Girl Scouts were formed with an ethos to be "non-sectarian in practice as well as theory."

By 1956, they were fully desegregated and Martin Luther King called them a "force for desegregation." Sarah Randolph Bailey was a trailblazer for the Girl Scouts, opening an integrated summer camp for girls and her troops joined the broader movement in 1948.

So it is not wrong to say the the best way to engage in social justice in the scouting movement in the Civil Rights era was to be a woman.

Sources:

Macleod. Growing Character in America.

You're not going to hear a whole lot about this directly from the BSA, as they tend to erase/modify their history to always appear somewhat inclusive and progressive, despite also being a very conservative private organization.

However, according to the African American Registry, the first "Negro" Boy Scout troop was founded in 1911, and, according to this source, by 1936 there were almost 5,000 black Scouts.

The problem is that your question can't really be answered, since no one can quote a source on "the climate" in the Boy Scouts during the 60's and 70's. We have no public records of private leadership meetings during this time, nor any similar records from individual troops around the country. But hopefully at least these cited numbers can give you a indication that the BSA has always been, at least in theory, more on the "acceptance and tolerance" side of the "climate" - speaking broadly, of course.

You're not going to hear a whole lot about this directly from the BSA, as they tend to erase/modify their history to always appear somewhat inclusive and progressive, despite also being a very conservative private organization.

However, according to the African American Registry, the first "Negro" Boy Scout troop was founded in 1911, and, according to this source, by 1936 there were almost 5,000 black Scouts.

The problem is that your question can't really be answered, since no one can quote a source on "the climate" in the Boy Scouts during the 60's and 70's. We have no public records of private leadership meetings during this time, nor any similar records from individual troops around the country. But hopefully at least these cited numbers can give you a indication that the BSA has always been, at least in theory, more on the "acceptance and tolerance" side of the "climate" - speaking broadly, of course.