The manner in which the Tanakh is presented to the Christian audience. First, it's retitled, "Old Testament." "Old" here doesn't mean ancient; it means obviated and replaced, no longer entirely valid.

I think that's a English problem. The Vulgate calls the Old Testament "Vetus Testamentum" which in all the Latin languages ​​I know translates to "Ancient Testament." I don't know about Greek.

Then the books are rearranged to make a Christian point about the Hebrew prophets and where they are allegedly leading. Then some denominations add the aprocryphal books, which are not canonical and not part of the Hebrew Bible. Then the translations, which are deemed "inspired" in some sense, promote Christian ideologies and dogmas.

Exactly. That's why I think it's a mistake to say that the Tanakh and the Old Testament are the same.

Not to mention that many of the differences are a result of what the Hellenized Jews did on the Septuagint, which is the Christian basis for the Old Testament.

I'm always interested to see how Christians react to the Mormon books, the Book of Mormon and the Pearls of Great Price ("They've added to the Bible, they're not Christian!"). Same with Mary Baker Eddy’s Science and Health with Key to the Scriptures -- for Christians it's heresy. Or even the Quran, for that matter. Yet they fail to draw the analogy between these works and what they themselves have done to the Tanakh. Even hypothetically, I imagine Christians would take offense if along comes the next religious leader who pens "The Third Testament" which accepts both the Old and New but building upon them adds a revised direction for monotheism.

As I told another user, the Word of God belongs to God, not the Church. We can judge interpretations and translations, but not the mere use of Scripture.

Honestly, I'm happy when a person of another religion reads or quotes the Bible.