Officially they are not open to atheists/agnostics.
They are not open to people who do not believe in a higher power. It is the official position of the BSA, and has been since 1910 (the Mormons have nothing to do with it) that
The Boy Scouts of America maintains that no member can grow into the best kind of citizenship without recognizing an obligation to God. In the first part of the Scout Oath or Promise the member declares, "On my honor I will do my best to do my duty to God and my country and to obey the Scout Law." The recognition of God as the ruling and leading power in the universe and the grateful acknowledgment of His favors and blessings are necessary to the best type of citizenship and are wholesome precepts in the education of the growing members. No matter what the religious faith of the members may be, this fundamental need of the members should be kept before them. The Boy Scouts of America, therefore, recognizes the religious element in the training of the member, but is absolutely nonsectarian in its attitude toward that religious training. Its policy is that the home and the organization with which the member is connected shall give definite attention to religious life.
Despite the context we give this today, the word "God" does not refer to the God of the Abrahamic faiths, nor is it intended or used to ban non-theists (as opposed to atheists). Many Buddhists, who are members of the BSA in full standing, don't believe in a God but do believe that there's a higher power that causes you to be responsible for your thoughts and actions. That's fine by the BSA. It is nonsectarian and doesn't care if you are Hindu or hold to the tenets of Meher Baba or Zoroastrianism (both of which have religious medals that BSA members can earn and wear on their uniforms).
So, yes, there are people whose lack of religious beliefs causes them to be disqualified from membership in the BSA. What's the problem with that?
Unofficially too.