This is misleading. The earliest complete manuscript of the Masoretic Text is indeed about a thousand years old, but the textual tradition itself is much older. And the differences between the two when it comes to messianic prophecies are minor to non-existent and show no signs of some deliberate corruption of the text.

Also, “The Septuagint,” properly speaking, is simply the Greek Pentateuch. The word is sometimes used to describe the Greek Old Testament in general though. Regardless, it is not the case that Greek speaking Jews used some single compilation of Old Testament texts in Greek comparable to the Greek Bible of today. So differences in the canon are not reducible to “The rabbinic Jews omitted some texts in the Septuagint.”