My question is if that door is now shut?
What does scripture say?
Hebrews 1:1-2 1 God, after He spoke long ago to the fathers in the prophets in many portions and in many ways, 2 in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom also He made the world.
Acts 4:12 12 "And there is salvation in no one else; for there is no other name under heaven that has been given among men by which we must be saved.”
John 14:6 6 Jesus said to him, “I am the way, and the truth, and the life; no one comes to the Father but through Me.
I am not sure what you mean about the door being shut, but a right relationship with God the Father has always been through the Son. The Old Testament presented Christ and the New Covenant in types and shadows. The first promise of a coming Redeemer is seen in Genesis 3:15:
Genesis 3:15 15 "and I will put enmity between you and the woman, and between your seed and her seed; he shall bruise you on the head, and you shall bruise him on the heel.”
God made no other provision to have a right relationship with Himself other than through the Son.
Philippians 2:9-11 9 For this reason also, God highly exalted Him, and bestowed on Him the name which is above every name, 10 so that at the name of Jesus EVERY KNEE WILL BOW, of those who are in heaven and on earth and under the earth, 11 and that every tongue will confess that Jesus Christ is Lord, to the glory of God the Father.
Perhaps this bothers you (as it does others) because you feel God owes everyone a fair chance to believe in Him? I think this is Pastor Bob's position; that the tribal person on some remote island will only be judged based on the light that he has and not whether he heard the gospel and had the opportunity to accept or reject Christ. The fact is that God is not fair in the way we define fairness. He is not obligated to save any. The fact that He saves some is all of grace. Perhaps that is why many of the greatest missionaries (like Hudson Taylor) the post-Reformation world has ever seen have been Monergists. They understood that the Gospel is the means of salvation to all who believe, so they set out to bring its saving message to as many unreached people groups as possible.