Would this also allow a private organization to discriminate on a religious basis, e.g. could the Boy Scouts also prohibit Muslims, Scientologists, or Mormons from joining?
The answer is: it depends.
Federal anti-discrimination laws normally prevent discrimination by organizations based on race, gender, or religion, but there are a couple of notable exceptions:
Freedom of Religion: Law and precedent clearly holds that a church (or temple/synagogue/etc.) can discriminate among potential members based on religious belief, but this is covered by the Freedom of Religion portion of the 1st Amendment, not by the "freedom of association" portion. So if you can prove to the court that your private school or club is really a church, you can discriminate.
For example, there is a scout-like organization called the Royal Rangers that is, in its founding and in its practice, explicitly and overtly religious. They are closely tied to a specific Christian denomination, they meet in churches, and their curriculum and meetings include Bible lessons and prayer. As a religious organization, they have the right to include or exclude anyone they want.
Freedom of Association: If an organization doesn't qualify under freedom of religion, it still might be able to choose their membership based on the "freedom of association" you mention in your question.
The term you are looking for here is whether your organization is a bona fide private club. If you can prove that your organization is a "bona fide private club" (and it is also tax exempt), then you can keep women off your golf course, you can keep blacks out of your Moose Lodge, or atheists out of your scout troop.
(The opposite of a "bona fide private club", by the way, is a "public accommodation", which is an organization that, though privately owned, offers services to the general public.)
How exactly do the courts determine if a club is a bona fide private club? According to the official EEOC standards, this is based on:
- The extent to which it limits its facilities and services to club members and their guests
- The extent to which and/or the manner in which it is controlled or owned by its membership
- Whether and, if so, to what extent and in what manner it publicly advertises to solicit members or to promote the use of its facilities or services by the general public
In other words, to what degree does the club behave like a private club? Does it allow anyone to join? Or is it selective? Does it allow non-members to attend and participate in the same way as members? Or is it truly exclusive?
Think of it this way: if any random sandwich shop or corner store could have just put up a sign saying "private club, whites only" while continuing to serve (white) customers normally, then the Civil Rights Act would have been completely useless.
So yes, the Boy Scouts of America has been found to meet this standard, in State, Federal, and even Supreme Court cases. They are allowed to exclude atheists and agnostics, and if they decided to, other religions.
Other organization, however, don't always meet the standard.
The California State Supreme Court found in 1990 that the "Boys Club of America" didn't meet the standard of a "private organization", since they admitted all boys. They weren't "selective" enough. Instead, they were held to the same standard as a "business" under California law, which isn't allowed to discriminate. They are now the "Boys and Girls Club of America." (Note that this was decided based on state law, not federal, which can differ widely.)