I've heard it said that it takes more faith to believe that God doesn't exist, than to believe that He does. It's quite true. For if one believes that an organ as small as an eye can capture the sun and the moon, all on its on, great faith has been demonstrated.
Ironically, the Bible states “For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.” (Romans 1:20 NIV) http://bible.com/111/rom.1.20.niv
If people are without excuse, and know that God does exist, how can anyone " not believe". The Bible actually addresses this as well. “Yes, they knew God, but they wouldn’t worship him as God or even give him thanks. And they began to think up foolish ideas of what God was like. As a result, their minds became dark and confused.”(Romans 1:21 NLT).
In other words, some people refuse to acknowledge God despite the evidence, and resist worshipping Him as God. They worship other gods. People who reject God, think of foolish ideas of what God is like. Some say God accepts every religion and everyone has a place in heaven. Some don't want to accept the fact that God is holy and perfect and He hates our sin. Some say they are their own God.
But what happens when people reject the true and living God who so loved the world that He gave us His only Son Jesus to die for our sins; the God who created heaven and earth? (John 3:16, Genesis1)
“So God abandoned them to do whatever shameful things their hearts desired. As a result, they did vile and degrading things with each other’s bodies. They traded the truth about God for a lie. So they worshiped and served the things God created instead of the Creator himself, who is worthy of eternal praise! Amen.” Romans 1:24-25 NLT http://bible.com/116/rom.1.24-25.nlt
“For this reason God gave them up to vile passions. For even their women exchanged the natural use for what is against nature. Likewise also the men, leaving the natural use of the woman, burned in their lust for one another, men with men committing what is shameful, and receiving in themselves the penalty of their error which was due.” Romans 1:26-27 NKJV http://bible.com/114/rom.1.26-27.nkjv
“And even as they did not like to retain God in their knowledge, God gave them over to a debased mind, to do those things which are not fitting; being filled with all unrighteousness, sexual immorality, wickedness, covetousness, maliciousness; full of envy, murder, strife, deceit, evil-mindedness; they are whisperers, backbiters, haters of God, violent, proud, boasters, inventors of evil things, disobedient to parents, undiscerning, untrustworthy, unloving, unforgiving, unmerciful;” Romans 1:28-31 NKJV http://bible.com/114/rom.1.28-31.nkjv
How should believers respond to unbelievers who have refused to accept the true and living God? We remember. Remember that the righteousness of God is through faith in Jesus Christ to all who believe, and that all have sinned and come short of the glory of God. (Romans 3:22-23). Remember. All includes you and me too. Remember the greatest two commandments are to love the Lord your God with all your heart, soul, mind, and strength and love your neighbor as yourself.(Mark 12:30-31) Remember that you are God's ambassador.(II Corinthians 5:20) You represent the gospel of love. This is how believers respond to unbelief. We remember!