Your characterization of "using" the Bible is off the mark. Every lodge has as its center-point, the Volume of Sacred Law. This may be the Holy Bible (In the USA, The King James Version, Old and New Testaments, without addition or deletion). There may be one or more different VSLs on the altar. In Saudi Arabia, the Holy Bible and the Holy Qu'Ran, are side by side on the altar. In Singapore, there are nine(9) different VSLs on the altar. Belief in the Holy Bible, is NOT required for masonic membership. There are many masons, worldwide, who are of other religions, and these men do not accept the Holy Bible to be revealed scripture.
The Grand Lodge of Indiana, has recommended the following readings from the Holy Qu'Ran, to be read, when a Muslim takes the degree work:
For the Entered Apprentice Degree
And hold fast all together, by the Rope which God stretches out for you, and be not divided amongst yourselves; and remember with gratitude God's favor on you; for ye were enemies and He joined your hearts in Love, so that by His Grace, ye became Brethren; and ye were on the brink of the Pit of Fire, and He saved you from it. Thus doth God make clear His Signs to you: that ye may be guided.
For the Fellow Craft Degree
God! There is no god but He, -- the Living, the Self-subsisting, Eternal. No slumber can seize Him, nor sleep. His are all things in the heavens and on earth. Who is there that can intercede except as He permitteth? He knoweth what (appeareth to His creatures as) before or after or behind them. Nor shall they compass aught of His knowledge except as He willeth. His Throne doth extend over the heavens and the earth, and He feeleth no fatigue in guarding and preserving them for He is the Most High, the Supreme (in glory).
For the Master Mason Degree
Truly Strong is the grip of thy Lord. It is He Who creates from the very beginning, and He can restore (life). And He is the Oft-Forgiving, full of loving-kindness, Lord of the Throne of Glory, Doer (without let) of all that He intends.
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Freemasonry is a secular, man-made organization, that exists quite openly. The answer to your second question is "no". There are many Jewish Masons, Reform, Orthodox, etc. none of the men accept the New Testament as revealed scripture. These men are welcomed into our fraternity, notwithstanding.
The answer to the third question is: Mormon Masons, take their oath on the entire Holy Bible, Old and New Testaments, King James Version. Jehovah's witness masons are free to use the version of the Holy Bible they prefer. Hindu Masons, use the Zend-Avestas,etc. If this is a problem to you, then you should have nothing to do with Freemasonry. Men of many different religions, other than Christianity are welcomed and accepted. Masonry is a world-wide society of friends and brothers, united under the all-seeing eye of God.
Charles E. Martin 32° Mason from Kentucky