Well, that was obscure...

If you don't mind me speculating: you found this four-day old article while Googling "Robert Bork" in preparation for posting something about Supreme Court nominee proceeedings.

Regardless...

The issue seems fairly logical to me. Either:

-- the BSA is a private organization with a protected priviledge to insist that its members profess a belief in a supreme being (or beings -- as I recall, Hindus are included), in which case, they are open to the characterization as 'religious' and the questioning of Federal funding; or

-- if they are not a religious organization, they forfeit the priviledge to exclude atheists and pagans from their membership.

They cannot be both.