This is going to be a somewhat long response and it is only the tip of the iceberg, but here are a few passages of scripture that lead me to believe the way I do:
1 Samuel 16:7 "Humans do not see what the Lord sees, for humans see what is visible, but the Lord sees the heart.”
“Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven.” Matthew 7:21
And what is God’s will? The following passage clarifies this:
Micah 6:8 He has shown you, O mortal, what is good. And what does the LORD require of you? To act justly and to love mercy and to walk humbly with your God.
Luke 10: 25-37: 5 On one occasion an expert in the law stood up to test Jesus. “Teacher,” he asked, “what must I do to inherit eternal life?”
26 “What is written in the Law?” he replied. “How do you read it?”
27 He answered, “‘Love the Lord your God with all your heart and with all your soul and with all your strength and with all your mind’[a]; and, ‘Love your neighbor as yourself.’[b]”
28 “You have answered correctly,” Jesus replied. “Do this and you will live.”
29 But he wanted to justify himself, so he asked Jesus, “And who is my neighbor?”
30 In reply Jesus said: “A man was going down from Jerusalem to Jericho, when he was attacked by robbers. They stripped him of his clothes, beat him and went away, leaving him half dead. 31 A priest happened to be going down the same road, and when he saw the man, he passed by on the other side. 32 So too, a Levite, when he came to the place and saw him, passed by on the other side. 33 But a Samaritan, as he traveled, came where the man was; and when he saw him, he took pity on him. 34 He went to him and bandaged his wounds, pouring on oil and wine. Then he put the man on his own donkey, brought him to an inn and took care of him. 35 The next day he took out two denarii[c] and gave them to the innkeeper. ‘Look after him,’ he said, ‘and when I return, I will reimburse you for any extra expense you may have.’
To bring this old parable told by Jesus into modern-day language, substitute minister for priest, Christian for Levite, and atheist for Samaritan. God was showing that kindness and compassion win out over religious doctrine. It emphasizes his previous point that if we love God and other people will are walking with him as we should.
When Jesus healed people on the Sabbath and was criticized by religious leaders, he was showing that mercy and caring about others takes precedence over religious doctrine.
And this passage in Paul says to me that even if people have never read the Bible or heard of Jesus, they are still without excuse to do evil because he gives us a beautiful created world, along with a conscious and an ability to appreciate that beauty.
Romans 1:20: "For ever since the world was created, people have seen the earth and sky. Through everything God made, they can clearly see his invisible qualities—his eternal power and divine nature. So they have no excuse for not knowing God."
