The single biggest changer of facts from the Bible was Muhammad. Anything that didn't fit his narrative he changed claiming it to be fixing a corruption. For example, he changed who Father Abraham almost sacrificed from Isaac to Ishmael, and who Isaac blessed from Jacob to Esau, and a hundred other modifications to make it look like God's promise came down his side of the family tree.
He got away with it unchallenged until the Dead Sea Scrolls were discovered by secular archeologists in 1947 which proved that the scriptures in the Bible had not been changed for 2200 years. The Scriptures that Jesus endorsed as "unbreakable" that must be believed are hence proven to be the same today as they were then. Q.E.D.
At that point, intellectually you have to unravel all Muhammad's modifications to what you call impurities and abandon your claim that "the Bible changes all the time."
No it doesn't. There have been many attempts to produce translations that are slightly more accurate in nuances of words - but the original Greek and Hebrew have not changed at all. Those are the official Bible and the translations are merely the work of fallible scholars. Even so, not one nuance changes the key fact that Jesus claimed to be the Son of God and that believing that he died on the cross for all mankind was essential. (John 3:16-20) Not one translation refutes that key message - the Good News - The Gospel. Muhammad worked hard to change that, "surely they killed him not" and "God forbid that he should have a son."
Joseph Smith of the Mormons got caught the same way. He produced a false translation of something he called the Book of Abraham to further his narrative. Then archeologists learned how to use the Rosetta stone and caught him when it turned out to be an Egyptian burial manual called the "Book of Breathings".
I understand it is hard to know the truth when it has been passed down so long. Thank God for storing the Dead Sea Scrolls in a cave outside Jerusalem for us as an independent check on the claims that have been made since then. This of course includes many of the false teachings of the Roman church that have crept into Christian teachings since about that same date in 610 when Pope Gregory the Great started adding his own preferences to the teachings of Scripture.