The New Testament book of Romans, written by Paul, very systematically deals with Jews and their system of law, and Gentiles, in relation to salvation.
Gentiles are dealt with first in chapter 1. Their paganism is utterly condemned. Jews are dealt with next, they “make their boast of God...being instructed out of the law are confident they are a guide to the blind, a light to them which are in darkness. An instructor of the foolish, a teacher of babes,” 2:17,19,20.
But, even though Jews have the law, they have not kept it. The situation of both Gentiles and Jews being summed up by saying: “We have proved both Jews and Gentiles, that they are all under sin. There is none righteous, no, not one” 3:9,10 Jews are as much sinners as the pagan Gentiles.
Whats the answer to this sad situation? “The righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: FOR THERE IS NO DIFFERENCE. FOR ALL HAVE SINNED, AND COME SHORT OF THE GLORY OF GOD.” 3:22,23.
So, yes, according to Romans, “the Vatican is wrong, Jews do need Jesus for salvation.” Likewise, yourself, and all Jews.
Christ said, “I am the way, the truth, and the life, NO MAN - which means all men, including Jews - cometh unto the Father, but by me,” John 14:6. Whether Jews or Gentiles, faith in Jesus Christ is the one and only way to God.
Believe as you wish, I do not share your stated beliefs (except the particular one that says that we are all sinners - that is undoubtedly true). None CAN be perfect - we were quite purposely designed to be very IMperfect, but with the capacity to improve. The extent of one’s improvement, given the totality of one’s upbringing, education and experiences - THAT is the measure of a person’s life, a measure that only G-d Himself can make.
I will not give up the faith of my fathers in the G-d of Abraham, Isaac and Jacob - ever, period. The more that I experience life, and the more that I study these matters, the more that my faith is reinforced. FYI, being told that I cannot have salvation (i.e. I’m going to burn in the fires of Hell, with some big, nasty, horned and hoofed guy in a red suit sticking me with a pitchfork all the time - ha, ha, ha, ha!) without changing my beliefs doesn’t do anything but reinforce those beliefs.
Go in peace.