There are two ways to approach the [Christians] Xtians:
to expose them, which, without more means to turn them away from Judaism or to politely but emphatically teach/tell them the truth and recruit them as counter-missionaries.
I think there can be an analogy to the passuk (Devarim 20.15) “Thus shalt thou do unto all the cities which are very far off from thee, which are not of the cities of these nations.” The essential question is, “how close are they in their ‘theology’ to the Torah?
First, One might start with the passuk: “Our fathers have inherited lies….” Jeremiah 16.19 (Hillel taught that one should draw people close to HaShem! Shammai drove the “potential” convert away with his staff.) Of course I am not encouraging seeking converts but because a distinction can be made between the Messianic (born Jews), (one whose theology, while skewed, is close to Torah) and the Catholic (whose theology permits avodah zarah, e.g. prayer to Yeshki, intercession of saints, baptism of the dead, transubstantiation etc. and is far away from Torah); one must try and first get the “Messianic Born Jew” to make t’shuvah (draw them closer to Torah observance e.g. abandoning Xtian theology) and for the Catholic to TURN towards HaShem as a Noachide. Just saying since it makes more sense to make peace/friends/ or “tributaries” (like King David) than making enemies. 2 Samuel 8:1–8:14, And the L-RD gave victory to David wherever he went.
The second point after starting with Jeremiah 16.19 is to prove that “G-D is not man, that He should lie” – if you prove that Yeshki lied, or rather prophesied falsely, then you have won the battle: the Xtians cannot get around Yeshki’s false prophesy in Matthew 16.28 and Luke 9:27. The Kingdom of David was not restored to Israel before Yeshki’s disciples’ death. To establish that Yeshki was/is not G-D simply show that he was not all knowing (Omniscient) as demonstrated by Acts 1.6, 7, and that he is not eternally co-equal with G-D, that is, he is not all powerful (Omnipotent) as demonstrated from 1 Corinthians 15.28 (G-D cannot be in submission or subjection to anything or anyone. This same scripture shows that Paul viewed Yeshki as a lord, not as L-RD. Moreover, use Yeshki’s own words to condemn Xtian theology: For example, he said, “The Father is Greater than I” and he is said to say, in prayer no less, “My G-D, My G-D why have you forsaken me?” Does G-D pray to G-D?)! Use their own scripture (and a little of their own honesty) against them. Use questions to show why their theology is wrong. For instance, ask why their is a contradiction between what the Torah says about the 70 descendants of Ya’acov going down to Egypt and what Acts says about 75 souls going down to Egypt: First get them to admit there is no contradiction in the truth and that the Xtian scriptures (which came after the Tanak) must line up with the Tanak (or must be rejected as contrary to the truth)! Deuteronomy10:22 Your forefathers who went down into Egypt were seventy in all, and now the L-RD your G-D has made you as numerous as the stars in the sky. Acts states that Seventy Five souls went down into Egypt. Acts 7:14
Since the math does not add up – that is, there is a contradiction between Devarim and Acts, one must stand on the Torah and reject (“push aside with a weak straw”) Xtian scriptures – the same with Yeshki’s false prophesy in Matthew and Luke about restoring the Kingdom – history does not lie! In fact, Paul writes in Romans (11:8) that the Israelites are blind and deaf; (to quote the NIV: “as it is written, G-D gave them a spirit of stupor, eyes that could not see and ears that could not hear, to this very day.” cross-referencing to Deuteronomy 29.4, Isaiah 29.10) and that “spiritual blindness has happened to Israel [….]” (Romans 11.25) this contradicts the passuk – Devarim 29:3 “But Hashem has not given you a heart to know or eyes to see or ears to hear until this day.” The phrase, “until this day” is limited in time to the day Moshe said, “This day, you have become a people [to the L-RD your G-D]” (Deut. 27:9).