Using this reasoning, Powell could also argue that any teacher who has a belief in God shouldn't be allowed to teach in her son's school district.
I don't see the connection. The BSA teaches Scouts that they should have a belief in some kind of God, or at least some kind of ethical/moral system wherein the doctrines/basic beliefs have at least some divine inspiration. Whereas a teacher who believes in God can work in the schools his or her entire career without once mentioning Him.
Having said that, I believe that allowing the BSA, GSUSA, and other organizations that require their members to believe in God to hand out recruitment flyers, etc., in the schools doesn't violate the First Amendment as long as the religious component of their program itself isn't being conducted at the school during this recruitment process.
In fact, it is a strict rule in the BSA that no Scout who is a member of a given unit can be required by that given unit to participate in any kind of religious ceremony.