This must be recognized as the most polarizing and foolish argument in all of Freemasonry. Why would I say this? Well, first of all, the inspirations if not the direct origin of Freemasonry clearly lies in the Pre-Christian traditions of Egypt, the Middle East, and Europe.
Officially, Freemasonry is adogmatic - even "mainstream" Freemasonry claims that the Grand Architect of the Universe, the GஃAஃOஃTஃUஃ is a symbolic term which may represent the deity of any religion, or the creative force of the Universe for those who do not care to anthropomorphize their deity.
However, in the late 19th Century, in the heat of the delusional mindset of the "Victorian Error" against which the western world is still struggling, the Anglophone Masonic organization, ever in search of excuses to express their distaste for their French brethren, used the removal of the assertion of a belief in deity by the GODF to deny them recognition.
Their objection to this change represents a political fiction. If it had the appearance of credibility at the time, it has long since ceased to appear sincere.
There are plenty of Freemasons in the Liberal Obediences who are sincere believers in one or another religion. Although "mainstream" obediences require that their members espouse a belief in a divine creator, it is inconceivable that no mason has ever either intentionally lied about this in order to gain admission to their lodges, or has so sworn in spite of serious private reservations concerning their own beliefs, or who, having later ceased to hold such beliefs, maintained silent concerning their loss of faith out of convenience. Beyond that, it is quite common in all times for people to espouse belief who are fundamentally casual and indifferent to the matter, practicing religion as a social convention alone. Such people will swear a belief in God without having really given the matter any serious thought.
Regardless of all this, the matter is folly. There is no justification for refusing to recognize one or another obedience for matters of individual dogma. Freemasonry is Freemasonry, and given the overall decline of the craft in modern times, we need to seek a more open and accepting approach to other obediences. The only truth behind this is one of callous political self-interest.
Today, in much of the United States, the belief in a supreme deity is an excuse for religious bigotry, intolerance, and most recently, literal witch hunts. While it may be wise to make the belief optional since even Grand Masters are guilty of both misinterpreting it and abusing it to forward their own more narrow beliefs, at the very least it is no excuse for not accepting that other groups exist with an equal right to bear the name "Freemason."
Change is long overdue.