As I said before, I lived on Kibbutz Einat, 15 miles northeast of Tel-Aviv, for the entire summer of 1975, so don't tell me I haven't been there. However, looking for mangers to see what they were made from was not high on my priority list. That's something you apparently did, so you could have a reason to condemn Christians who often portray a nativity scene with a wooden manger. As I said, we visited many sites, Tel Aviv, Akko, Nazareth, the Sea of Galilee, the Jordan River, Jerusalem, Bethlehem, Mt. Carmel, Eilat, the Dead Sea, Masada. I don't recall seeing any mangers at all. There were none (that I saw) on the kibbutz. Although historically there were wooden mangers and stone and clay, no Christian that I know believes that the nativity scene is a totally accurate picture of what it was really like when Jesus was born. Nobody knows for sure, no, not even the Jewish people.
This may surprise you, but the Jews do not have a corner on Biblical knowledge. In fact, if they have not accepted Jesus as their Messiah and Lord, then they do not even understand the Old Testament, much less the New Testament. Paul tells us that in 2 Corinthians 3:14-16:
"But their (the sons of Israel) minds were hardened; for until this very day at the reading of the old covenant the same veil remains unlifted, because it is removed in Christ. But to this day whenever Moses is read, a veil lies over their heart; but whenever a person turns to the Lord, the veil is taken away."
So if you want true knowledge about the Bible, either the Old Testament or the New, don't ask a Jewish rabbi, unless he has received Jesus as his Messiah and Lord. Even then, some messianic Jews, before they came to the Lord, were so steeped in rabbinic teaching and the Talmud and the Jewish traditions, etc. that they can't see how the teaching in the New Testament contradicts much of what they have learned. Unfortunately some immature Christians think that the closer they get to Judaism and all things Jewish, the closer they get to God. It's just the opposite. Paul himself was steeped in Judaism but listen to what he said after being saved:
" ...If anyone else has a mind to put confidence in the flesh, I far more: circumcised the eighth day, of the nation of Israel, of the tribe of Benjamin, a Hebrew of Hebrews; as to the Law, a Pharisee; as to zeal, a persecutor of the church; as to the righteousness which is in the Law, found blameless. But whatever things were gain to me, those things I have counted as loss for the sake of Christ. More than that, I count all things to be loss in view of the surpassing value of knowing Christ Jesus my Lord, for whom I have suffered the loss of all things, and count them but rubbish so that I may gain Christ, and may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith, ..." Philippians 3: 4-9