After the destruction of Jerusalem circa 70AD, the remaining Jews were very concerned about the preservation of their culture. Of particular concern to them was Hellenization, which is a term for, essentially, Greek cultural influence and assimilation into said culture. Now, of course, one might note that the Jews in what had been Israel had actually fallen under the influence of the Roman empire, and that the Jews outside of Israel were also predominantly residing in the Roman empire, however, the eastern parts of the Roman Empire were actually predominantly culturally Greek. This is why, for example, when we speak of the early Christian church, what today are the Roman Catholic areas are often referred to as the Latin church, and what today are Eastern Orthodox areas are often referred to as the Greek church, even though almost all fell under the aegis of the Roman Empire, and in fact the Roman capitol even more to the east at one point, the city of Constantinople, which sort of eventually became the Byzantine Empire, though with lineage straight back to the Roman Emperors and pro-consuls of old.
In any event, prior to Jewish rabbical councils sometimes between 70-100AD, a lot of books were read in Jewish shuls (aka synagogues), and some would include the deuterocanonicals and some would not. There was no canon of scripture for in the sense of the term Christians would use it. And, it was not a particularly pressing issue that some Jews were more hardline about only using scriptures written only in Hebrew and others would happily include scriptures that may have originally been written in Greek. After all, many Jews were living outside of Israel in predominantly Greek areas, and if some of those Jews had transcribed oral tradition into scripture, well, they weren't any less Jews than the other Jews.
However, this landscape was changing with the sacking of Jerusalem. Suddenly, Judaism as a culture and as a religion seemed to be in danger of dying out. And it would die out not through a simple genocide, but through a gradual loss of faith and culture over generations as children adopted the cultures around them. In fact, retroactively, some rabbis and others became concerned that this had already been happening even while Jerusalem stood due to foreign rule and foreign cultural interchanges. And, of course, there was Christianity, which from their perspective was essentially a false Greco-Roman version of Judaism for Greco-Romans.
So, there was this huge impetus to figure out what was to them genuine Jewish culture and religion and then define it and freeze it and eradicate outside influences. In this way, much as kosher laws earlier had served to preserve Judiasm as a separate culture and faith, they would hope to preserve historical Judiasm for centuries to come. So, the Greek deutrocanonicals, to the extent they had been in, were out. Not Hebrew. They wanted Hebrew. They wanted stuff that was absolutely free of outside of influence.
Now, of course Christianity to them was part of this Hellenization they were concerned about, but I wouldn't say they ditched the duetrocanonicals *because* of Christianity. I'd say that the duetrocanonicals and Christianity, from a Jewish perspective at the time they canonized scripture, we symptomatic of the same cultural drift and cultural threat. Two fruits from the same poisoned tree, as it were, rather than one being bad because of the other one.
Of course, from a Christian perspective, the authority to define scripture passed from Judiasm to the Church in 33AD or so when Jesus died, rose again, and the Holy Spirit descended on the Apostles to lead the Church on earth. So, when a council of non-Christian Jewish rabbis made a ruling to exclude the duetrocanonicals 40-70 years later, form a Christian perspective that wasn't really their call to make as it regarded the Christian bible. It was the province of the Apostles, and, when they died out, the Bishops. And of course the Christians were not going to toss out the Greek Old Testament books- the entire New Testament had been written in Greek. Many Christians were Greek or Greek influenced. Jesus is depicted as quoting Greek translations of the Old Testament in the New Testament several times (Though he actually was quoting them in Greek when he walked the earth is extremely questionable, he was probably speaking Hebrew or Aramaic). The factors that caused the Jews to throw those books out were not present in the early Church and in fact the early Church would have sort of been fighting in the opposite direction in general.
Also, The Book of Tobit is cool.
