So, the innovation afforded by Martin Luther, which excluded certain books, (he had also wanted to exclude James and Revelation, among others) has nothing to do with which Bible Baptists use today?
Nothing at all. Luther's musings have not been followed even by the Lutheran churches.
The canon was identified these times around the fourth century: the Synod of Rome, 382, the Council of Hippo, 393, the Council of Carthage, 397, a letter from Pope Innocent I to Exsuperius, Bishop of Toulouse, 405, and the Second Council of Carthage, 419. It is the same Bible Catholics use today.
In fact, for 1100 years, until Luther came along, Christians used this Bible.
I thought nothing could be added to or taken away from the Bible?
Nothing can be, but that has not stopped the Church of Rome.
The Lord Jesus and the Apostles never quote from the Apocrypha, though they certainly has access to it.
Josephus and the Talmud are clear that The Apocrypha was never part of the Jewish Scriptures.
Philo, the Jewish philosopher, quotes from all but five O.T. books; never from the Apocrypha.
None of the writers of the Apocrypha claims divine inspiration or origin.
Some parts of the Apocrypha contain blatant errors of historical fact; other parts contradict the O.T.
In AD 170, Melito, leader of the church at Sardis, travelled to Jerusalem to ascertain the true O.T. canon, He came back without the Apocrypha.
Jerome, who translated the Vulgate, wanted to exclude the Apocrypha. The O.T. that Protestants use today is identical to that upheld by Jerome.
Cardinal Ximines excluded the Apocrypha shortly before the Council of Trent when it was formally adopted.
The name 'Apocrypha' means 'hidden things, because it was not read out in early church services because it was not regarded as true Scripture by the early Church.