There are some issues with this.
The Masoretic Text (is that the "Majority Texts") was put together between 600-900 CE, or at least three centuries after available copies of LXX were produced, or almost a thousand years before LXX was completed.
Yes, however the dead sea scrolls are much older. Some of them match the Masoretic text fairly well. Some of them do not, however. That suggests that there were textual variations even around the 1st Cent, but that they were not created by the Masoretes.
Is this the claim: copies of the LXX, which were produced three hundred years after Jesus died, are versions that were altered to support Christianity, and the evidence is that they don't coincide with the contents of the Masoretic Text, which was put together three to six hundred years after, and are supposed to come closest to the original Hebrew Bible?
I'm not convinced that there were many changes to either text for Christian or Jewish purposes. As noted above, it appears that there were multiple versions of the Hebrew even in Jesus' time.
The problem with the LXX is that in addition to being based on a different text, the translation is of varying quality. Some of it seems pretty free. In several books it's substantially shorter. There are also other ancient translations that are worth looking at. E.g. the Vulgate seems to have been from something like the MT, and was made before the currently available MT manuscripts. There's also another Hebrew text: Samaritan.
Early critical translations tended to follow just the Masoretic text. Today, the Masoretic text, the LXX, and the Dead Sea scrolls are used together. However many current translations probably emphasize the MT more than experts would today. One of the changes in the Updated Edition of the NRSV will be reconsidering the OT text. (I'm guessing the new edition will be published in 2022.)
Here's a useful summary of the situation.
Old Testament Textual Criticism. As you'll see, it's a lot more complex than the discussions here have suggested. Remember, I'm not an expert in the area, which means I don't know the author. But from what I know, I'm going to guess that this reference is more reliable than the discussion here.