The two genealogies, Matthew's and Luke's, work in harmony to provide an accurate explanation of how it is possible for Jesus to be both a descendant of David, and the Son of God. I can't imagine any Jew would accept a Messiah whose genealogy to David was not beyond doubt
It is doubtful that many Jews give any credence to either Matthew or Luke. They are looking for a king (anointed), who will lord over the nations/Gentiles (Zechariah 14:16) and shepherd Israel, the combined tribes of Ephraim (the 10 northern tribes) and Judah (the 3 southern tribes, including Levi (Ezekiel 34:22-24 & 37:22-24)). That hasn't happened, and will not happen until the "end of the age", when the "tares", including the Gentile church, those who "commit lawlessness", are gathered and thrown into the furnace of fire" (Matthew 13:39-42)
Matthew list 42 generations from Abraham to the time of Christ, yet there aren't 42 named. As for the message of Yeshua, to be a "son of God", one must do the will of God. The god of Christianity is Paul, and he is a son of Benjamin, according to Paul. Another son of Benjamin, was king Saul, Paul's predecessor, who tried to kill David. Paul tried to kill Yeshua's followers, but as with king Saul, he failed. Those who claim killers of saints as their fathers, such as Paul, will wind up having the blood of the saints on their heads. (Matthew 23:29-35).