Apparently, there is some controversy about the actual reading of Matthew 28:19, which I read as: Go therefore and disciple all the nations, baptizing them into the name of the Father and of the Son and of the Holy Spirit. (RcV)
But the arguments surrounding this verse are misleading for two main reasons. First, there are plenty of old texts of the New Testament, both Greek and translations, that contain this verse as written, some of which predate AD 300. There are no manuscripts or versions (i.e. translations) of Matthew that contain a different reading. This is easily verified by studying the critical apparatus in Novum Testamentum Graece 27th ed. compiled by Nestle and Aland. God sovereignly arranged for the existing manuscripts of the New Testament to be preserved, discovered, and studied, and I appreciate the scholarship that gives us an amazingly accurate text of the New Testament. Furthermore, difficult readings (such as this one) are actually somewhat common in the New Testament, and it is a tenant of textual criticism to take a more difficult reading over an easier one.
Second, and more importantly, one of the items of our Christian faith is that the Bible is the Word of God. Based on our being infused with Christ Himself as our faith when we believed into Him, we similarly believe God's Word as we have it. Advancing ideas that require one to doubt the actual text of the New Testament, replacing it with unsupported alternative readings undermines this belief. Unfortunately, such "analysis" is usually based on a certain theological predisposition, which does not match the Christian faith at all.
So in sum, those who are healthy in the faith should have no problem with such arguments, as they spontaneously believe God's word and reject alternatives to it. But, as believers, it doesn't hurt to be aware that both according to the historical record (Biblical manuscripts) and according to the faith delivered once for all to the saints (our Triune God embodied in Christ realized as the Spirit infused into us), Matthew 28:19 will read as it does for eternity.
Matthew 29:19b-20a; Codex Vaticanus (ca. 4th century). Courtesy of The Center for the Study of New Testament Manuscripts - www.csntm.org and images.csntm.org/Manuscripts/GA_03/GA03_024a.jpg for the text.