If the people you are talking about believe exactly what you wrote, then they are wrong, but there is some truth in it. The blessing and cursing comes from Genesis 12:3 "And I will bless those who bless you, And the one who curses you I will curse. And in you all the families of the earth will be blessed.” The verse doesn't refer to salvation, but attacking or treating Israel as the root of all evil would probably fit in with the curse of this verse.
In Daniel 9 "24“Seventy weeks have been decreed for your people and your holy city, to finish the transgression, to make an end of sin, to make atonement for iniquity, to bring in everlasting righteousness, to seal up vision and prophecy and to anoint the most holy place. 25So you are to know and discern that from the issuing of a decree to restore and rebuild Jerusalem until Messiah the Prince there will be seven weeks and sixty-two weeks; it will be built again, with plaza and moat, even in times of distress. 26Then after the sixty-two weeks the Messiah will be cut off and have nothing, and the people of the prince who is to come will destroy the city and the sanctuary. And its end will come with a flood; even to the end there will be war; desolations are determined. 27And he will make a firm covenant with the many for one week, but in the middle of the week he will put a stop to sacrifice and grain offering; and on the wing of abominations will come one who makes desolate, even until a complete destruction, one that is decreed, is poured out on the one who makes desolate.” it talks about 69 weeks, then the Messiah and then 1 week (7 years). This prediction is about Israel. It was exactly 69 X 7 years from the declaration of Artaxerxes to Jesus riding into Jerusalem on Palm Sunday. Then there is a break in the history of Israel with the creation of the church. The church age ends at the rapture of the church.
(1 Thessalonians 4) "16For the Lord Himself will descend from heaven with a shout, with the voice of the archangel and with the trumpet of God, and the dead in Christ will rise first. 17Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord."
Then the final week of Israel happens which is the 7 year Tribulation. Lots of verses suggest there will be converts to Jesus during the 7 year Tribulation, meaning there will be new Christians (Jew & Gentile) during this time and many (most?) will be martyred.
At the final coming of Jesus, of those still alive (50% or less of the population at the beginning of the Tribulation since two of the judgements are 1/4 and then 1/3 being killed) Jesus will judge those who are still alive in the sheep and the goats judgement.
Matthew 25 says, "31 “But when the Son of Man comes in His glory, and all the angels with Him, then He will sit on His glorious throne. 32All the nations will be gathered before Him; and He will separate them from one another, as the shepherd separates the sheep from the goats; 33and He will put the sheep on His right, and the goats on the left.
34 “Then the King will say to those on His right, ‘Come, you who are blessed of My Father, inherit the kingdom prepared for you from the foundation of the world."
At the final coming of Jesus, the Jews that remain will come to know Jesus as Savior. (Luke 13:25)"Behold, your house is left to you desolate; and I say to you, you will not see Me until the time comes when you say, ‘Blessed is He who comes in the name of the Lord!’ ”" (There is another verse that says it even clearer, but I can't remember it at the moment.)
Like so many things people say about Jesus and the Bible, there is some truth, but many people take a truth and stretch it in one direction or another. Saying "Israel is our way of Salvation" is totally wrong, but also saying, "Israel is no longer important" or that "Israel is the root of evil" is just as wrong.