There is nothing in the New Testament that supports this.
Since God is just, everyone has an opportunity to receive the Light. This is one of the true names of Christ. (I AM the Way, the Truth and the Light.) You are judged by the Light you have received.
Revelation 5:9 also speaks of the universal availability of the salvation from Christ:
"...with your blood you purchased for God those from every tribe and tongue, people and nation."
Clearly there are many tribes, tongues, peoples and nations which had already died out and were extinct before the coming of Jesus Christ, and many, many more which became extinct over the last 20 centuries without ever hearing the name of Jesus Christ. Are they all damned? By no means! Because every one of these people, every person who "comes into the world," can be enlightened by the Light. Can repent and believe. Can choose the Light, Who is in fact the one Mediator between God and the human race: Jesus Christ.
This is not universal salvation. This is the universal availability of salvation. 1 Tim. 2: 3-4 This is good and pleasing to God our savior, who wills everyone to be saved and to come to knowledge of the truth.
What about the Syrophoenician Woman? (Mark 7:25-30/Matthew 15:21-28)
They have their own religion.
Homos as Priests and now this - unbelief and you're still "saved" - totally UnBiblical.
You must not have read Romans....
"I am the way, the truth and the light; no one comes to the Father but through me."
You can either take that as "You must believe in Jesus," OR "Jesus is the bouncer at the gates of Heaven"--that Jesus alone determines who gets in--among those who believe and those who don't.
John 6:44,45
More people need to follow the example of the Bereans (Acts 17:11), who searched the Scriptures daily to find out whether what they were being told was so.
Galatians 1:8-12