I’ve been comparing some “Messianic passages” from the Tanakh (the Hebrew Bible) to the corresponding verses in our Christian Bible (KJV, NKJV, NASB).  And I’ve noticed that, in many passages, the Tanakh translation differs significantly from our OT/NT translations.  Psalm 22, Isaiah 53, and Zechariah 12, for example, are quite different in the Tanakh, compared with the Christian Old Testament (and the New Testament references to the OT messianic verses).  To take an example, here is Zechariah 12:10 in the KJV:  “…..and they shall look upon Me whom they have pierced.”  And here is the same passage in the Tanakh: “…..and they shall lament to Me about those who are slain.”  How do we account for differences such as this? Which is more accurate, the Hebrew bible or the Christian bible? And might there have been an intentional effort by English translators of the Tanakh to “water down” the passages that fit the person of Jesus? (Or might the translators of our Bible consciously or unconsciously skewed their translation towards an identification of Jesus as the subject of the “messianic verses”?)  This issue has troubled me for quite a while. Thank you for reading this!

First of all, you say that you are reading the Tanakh (the Hebrew Bible), but you are quoting in English.  So, I need your help to make your question clear.  If you are quoting in English, this means to me (but I might be wrong here) that you are not reading the Hebrew Tanakh, but perhaps you are reading  Jewish-sponsored translation of the Hebrew scripture.   Is that the case?  I will assume so as I answer below.

Second, it is entirely possible and even quite likely that English translations sponsored by Christians will be biased toward a Christian interpretation that certain Old Testament passages are prophecies of Jesus of Nazareth.  Also, it is entirely possible and even quite likely that a Jewish translation of the same Hebrew Old Testament will be biased against the Christian interpretation that the passage is either messianic or applies to Jesus.  Your premise is certainly a reasonable one.  Let me go farther–it is almost certainly true.

Third, when the writers of the New Testament quoted from the Old Testament, they often used the Greek Septuagint rather than the Hebrew text, which can quite possibly skew the Greek New Testament quotes away from a literal translation of the Hebrew Tanakh.  This is famously true with Isaiah 7:14 where the Hebrew has a word best translated as young woman, but the Septuagint has a Greek word which is unambiguously a virgin (which is not surprising as the prophecy refers to the birth being a miraculous sign).

Here is my response to the generic problem you raise.  What you or anyone else can do is we can go to the original Hebrew and ask what the most reasonable translation is, regardless of whether we are looking from a Jewish or a Christian perspective.  Let us apply that to Zechariah 12:10.  I am looking this passage up in my Hebrew interlinear.  I invite you to do the same at this link:  https://biblehub.com/interlinear/zechariah/12-10.htm    Here is what I find:  The relevant Hebrew word is daqaru (anglicized).  The word daqaru means pierced, not slain.  The word slain in an interpretation, whereas the word pierced is a fairly literal translation.  Therefore, in this particular case (althought my research here is a bit shallow–just a first go), the “Christian” translation seems to be the more accurate one, and we can accuse the Jewish translation you have used as being biased.

Here is my guess:  If you do a deep dive, you will find a few examples of “Christian” translations which are at least somewhat biased toward the Christian interpretation that these passages are predictions about Jesus.  You will also find that Jews have applied a similar bias, but in the opposite direction in order to oppose the Christian interpretation of some of these passages.  My guess is this (but it is a bit of a guess, based on a few experiences, not a scientific analysis).  My prediction is that you will find more examples of Jews trying to avoid the Christian conclusion than vice versa.  Zechariah 12:10 supports my prediction.  I believe that you are on the right track here, in that you are applying a healthy level of skepticism toward your own Christian faith. This is what we ought to do for two reasons.  First of all, our opponents will certainly do the same thing, and we need to be prepared to answer such criticisms.  Second, we ought to do this because we have nothing to fear!  Jesus Christ is the Messiah.  Christians are right on this question.  Therefore, if we are right, then a thorough investigation of all questions will favor the thing we already have faith in, which is that Jesus is the Son of God, the Messiah, the one sent by God to save the world from their sin.

John Oakes