Celestial Lodge Above is generically referring to Heaven. The same way we may say “Grand Architect of the Universe” as a universal term for God.
See - as stated and easily researched, to be a Mason one must believe in a higher power. See as we accept a man OF any faith, we endeavor to do improve ourselves, eachother and the world around despite our differences in faith, religion, nationality, race or political affiliation.
What other organization can make such a claim?
The crux of the argument was whether Masonry was a religion or held certain religious beliefs. I think you are supporting the side that says it is or does.
See as we accept a man OF any faith
But there must be some faith - in a higher power, God.
I think Masonry also teaches that all faiths are equal or the same in value - it's up to the individual. This is contrary to Catholic teaching, and part of the reason one cannot be a Mason and in the Church (except illicitly of course).
This isn't meant as a slam to any particular Mason, but an explanation of the whats and whys as far as the Catholic Church and Masonry. One can and must choose if the choice occurs.
What other organization can make such a claim?
As far as religious institutions, the only one that comes to mind is Universal Unitarianism, though last I looked, atheist and agnostics were welcomed - which wouldn't be the case for Freemasonry.
Thanks very much for your courteous reply.