Steve Ray has a list of 35 loaded Questions for "Bible Christians" (quotation marks his)(link to the whole list). This is number 23/35. I'm trying to provide the answers in a common format, for easy reference.
23) Why do Protestants follow postapostolic Jewish decisions on the boundaries of the Old Testament canon, rather than the decision of the Church founded by Jesus Christ?
This question is so loaded that the only simple answer that can be given is "they don't."
1) We follow, in the strongest sense, the canon to which Jesus referred when he said, "from Abel .. unto ... Zacharias." (Matthew 23:35 & Luke 11:51)
2) The Roman Catholic Church is not "the Church founded by Jesus Christ."
3) The decisions of various local councils in the first millenium were not decisions of "the Church" that would require anyone outside their jurisdictional boundaries to do anything. They are decisions of churches, but not of The Church.
4) There is more than one sense to "follow." We agree with the Jews regarding the canon, but that's not quite the same thing as "following" them in the way that we "follow" our leaders.
5) The post-apostolic Jewish views of the canon provide evidence regarding the Old Testament canon. It would be foolish to ignore that evidence, and the church fathers themselves did not all ignore that evidence.
6) Some scholars allege that there was a so-called "council" of Jews at Jamnia that established the current Hebrew canon (as with so many other things in ancient history, other scholars disagree). While this so-called "council of Jamnia" of about A.D. 90 may have come after the death of the apostle John (normally thought to have died about A.D. 100), its constituent Jews were naturally those who lived during the apostolic period. So, "post-apostolic" (if it is referring to Jamnia) is misleading.
7) It is frankly absurd to imagine that no one had any idea of what the canon of Old Testament Scripture was before the Incarnation. After all, when Jesus speaks to people in the Gospels he frequently refers to "the Scriptures" and even exhorts the Jewish leaders who doubted him to "search the Scriptures." They didn't reply, "But no one has provided us with an infallible canon yet!"
8) Suggesting that we should follow the decision of a post-reformation Roman Catholic council as to the Old Testament purely on the weight of its authority is troubling, given that the same council, in the same section refers to Hebrews as one of Paul's epistles, something that practically all Biblical scholars today (even Roman Catholics) recognize isn't accurate. In other words, we have no good reason to think that Trent was infallible or to accept its decision as a decision that should bind God's church.