"If this is really a good, full-proof argument against Protestantism, then what is there to stop a Jewish apologist from arguing the following:
"The Old Testament was written and canonized by the Jews. Therefore, if Christians want to consider the Old Testament divenly inspired, they must also consider the Jewish religion divenly inspired, including the Talmud and other Sacred Jewish traditions that Christians reject.
The OT was not "canonized" by the Jews." The idea that they did is historically fallacious. Rabbinic Judaism did not create a solid "canon" until the 1st century A.D. as a response to Christians who were utilizing the Septuagint and various Scriptures to support the Messiahship of Jesus. Before this, there was no set agreed upon Jewish Canon. There were simply collections of Scriptures that certain factions with Judaism accepted or didn't accept or use, that may have been more or less solid based upon the Jewish faction...but there was no standard agreed upon. This varied from place to place and tradition to tradition. For example, the Sadducees only accepted the Pentateuch, as did the Samaritans. The Essenes accepted many, many other Scriptures. What did the predecessors to Kabbalah accept? What about the Zealots? The Sciarii? etc. What did the Jews at the competing Jewish Temple of Leontopolis in Egypt accepted? Another temple you ask? Yes, another temple with a more legitimate claim to the High Priestly line, (but that's another story.) Christian (Messianic) Jews clearly accepted books such as the Assumption of Moses and Enoch, as well as other books referenced or alluded to in the NT Scriptures as part of their belief structure.
The canonization of any aspect of ecclesial life is a function of the Church - i.e. "the assembly" - of those who are legitimate heirs to Abraham - Isaac - and Jacob. Orthodox Christianity has always seen itself at the legitimate heir of the Jewish religion, and sees Rabbinic Judaism as a heresy - and vice versa. Unfortunately, most of us today see two different religions instead of two streams claiming the same origins. The question then becomes, after Jesus - which strain of Judaism (Christianity or Rabbinic Judaism) actually represents the legitimate continuation of Israel. The NT continuously tells us that it is those who are Christians who are truly "Israel" - whether Gentile or Jew. "That is, it is not the children by physical descent who are God's children, but the children of the promise are considered to be the offspring." Romans 9:8.
The establishment of the "canon" for Rabbinic Judaism was a result of Rabbi Akiva Ben Joseph sometime around 90 A.D. in response to the rise of Christianity.
How the various Churches came to their canons is another story altogether; but the reality is that Judaism did not set their own "canon" of the OT until the destruction of the Temple and as an attempt to combat the "heresy" of Christianity. Even then, they allowed changes to be made by Masoretes using the Halakha process of the "Tiqqun soferim" - the "restorations of the scribes" which allowed small changes to be made to combat heresy. This was the beginning of the process of intentional corruption of the Masoretic text to combat Christianity.
I could recommend many books on the subject; like "When God Spoke Greek" by Timothy Michael Law...but the bottom line is that the Jews did not have a true canon in the way we know it today prior to the 1st century.
If the Church was already on the scene - and if you are a Christian - then Rabbinic Judaism has no valid claim to set the canon anymore than Marcion and the Gnostics did. It is the Church which defines what a proper "canon" is...and Rabbinic Judaism is not the Church.
Again, this doesn't even touch on our modern notions of "canon" verses what it meant in the early Church.