What happens to righteous people of other religions on judgement day, who never got to hear the Gospel of Christ?

The gospel of Christ includes the fact that nobody is righteous. That should be the starting-point for understanding why the Word of God left Heaven to become the man, Jesus, who would die to deal with all the sin of the world (Read John chapter 1).

Jesus came to do for unrighteous sinners what they could never do for themselves; be reconciled to God. The barrier between us and the righteous God is our sin - our unrighteousness. If you read Romans chapter 3 you will discover the fact that nobody is righteous. The nation of Israel, chosen by God to be a holy nation and a kingdom of priests, is not righteous. That standing before God, established at mount Sinai, did not result in them being righteous. Their own scriptures warned them of that, in Isaiah 64:7. But in Romans ch. 3 it goes on to say that all non-Jews suffer the same problem - that of being unrighteous.

Yet verses 21-30 show how God's righteousness was demonstrated through what Jesus did, in dying for the unrighteous. Part of it says, "This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, for all have sinned and fall short of the glory of God, and are justified freely by his grace through the redemption that came by Christ Jesus." That is the glorious good news that is all over the Earth, spread by Christians. The Holy Spirit is using that good news to reach those we cannot reach. All who are appointed to salvation will yet be saved, Jesus assured us (John ch. 17).

Ch. 4 in Romans goes on to show how Abraham was justified by God because of his faith in God, not any righteousness in himself. Keep reading to see how (in ch. 6 vs 18) those who respond in faith to the good news about Jesus are set free from sin and become slaves to righteousness, becoming slaves to God (vs. 22). A verbal hearing of the good news about Christ is but one way of learning the gospel. Some have just had a single page torn out of the Bible, and read that good news, responding in faith. Others have had dreams about Christ where not even a page of the Bible is available to them. The Internet is spreading the good news to places where Christians were never able to go. Do not fret about other people. Consider where you stand - have you responded in faith to the glorious good news about Christ? If so, devote yourself to sharing it, however the Spirit of God leads you, and have faith that "The arm of the Lord is not shortened, that it cannot save." (Isaiah 50:2)

They will be judged based on God's standards.

They will be taught the gospel before the judgement day. If they are good people, they will choose God who is good. They will know Him because they are familiar with the light that is in them or "true Light, which lighteth every man that cometh into the world." John 1:9

"For for this cause was the gospel preached also to them that are dead, that they might be judged according to men in the flesh, but live according to God in the spirit." First Peter 4:6

For when people of the nations, who do not have the Law, do by nature the things of the Law, these people, although not having the Law, are a law unto themselves.  They are the very ones who demonstrate the matter of the Law to be written in their hearts, while their conscience is bearing witness with them, and by their own thoughts they are being accused or even excused. Romans 2:14 -15

All goodness and love coming from God, those who are good and loving are pleasing in his eyes.

There are no "righteous people". We are all sinners.
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And judgment day is only for those that refused to believe in Jesus, and they are all sent to eternal torment in the lake of fire. Nobody can be saved on judgment day. It is too late to be saved, after death. Judgment day only confirms that you are unsaved. So the key is to avoid judgment day, and that is only by believing in Jesus.

And the Lord Jesus is God, and He will get the truth to everybody that wants the truth. Acts chapter 10 is the proof, with the account about Cornelius. So everybody is without excuse. Everybody that wants the truth, will find that Jesus will get them the truth.

Death leads to immediate heaven or hell, depending only on whether the person believed in Jesus for eternal life, or not.

Jesus loves you and wants to bless your life freely :) Most of all, Jesus wants you with Him forever, and not in hell. The truth is that every belief except one will lead to eternal torment in the lake of fire for every person. Because nothing pays for our sins except the death and blood of Jesus, the sacrifice of Jesus that is already accomplished by Him . Jesus loves you! The truth is that Jesus is God, and Jesus died on the cross to pay for all of our sins in full, and then Jesus resurrected from the dead. Nothing else pays for our sins, not works, not deeds, not religions. So the only way to heaven and to avoid hell, is by believing in Jesus for eternal life (John 6:47), without adding any of your own works (Romans 4:5). Believe in Jesus to take you to heaven, and you will be in heaven, no matter what, guaranteed. That easy, thanks to Jesus! Tell Jesus that you thank Him that you will be with Him in heaven when you die, because you believe in Jesus! It is too late to be saved, after death.

That is explained in Romans 2:14-16.

Romans 3:10 "as it is written, “There is none righteous, not even one;"

Simple.
They will die.

The bible says the gospel has gone out to all the earth. Yet the Christian God is just. Anyone going to hell will deserve it.

They all go on with their lives until their respective god decides it is time to finish.