Well, that is a confusing question because no real Christian would answer 'yes.' If you asked if a Christian can understand why someone would not believe in God, the answer would also be 'yes.'
People don't believe for various reasons. Some of them are a lack of perceived need, a lack of understanding about Who God is, a way of life that keeps God out, anger at God for a perceived lack of intervention by God or for things that have happened to the non-believer or others in their lives, the behavior of believers, inconvenience and preference for a "religion" that offers more flexibility and more of a self-centered approach to life.
Now, there are some people who believe in God that don't believe in Jesus Christ as the only way to Him. I can't speak for what they would say about believing or not believing in God.
I think God has given us a heart for Him, even if some cultures and some young people do not yet know Him.
He has said in His Word, "For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse." (Romans 1:20)
I don't know how God will judge those who have never had the opportunity to hear His word or read the Bible. I do know that God is absolutely just and loving and that whatever He does, it will be fair.
As for those who hear and don't believe, there will be judgement. Unfortunately for those people, the judgement is eternal separation from God in hell. But hell wasn't made for mankind, it was made for Satan.
"The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering toward us and not willing that any should perish, but that all should come to repentance." (2Peter 3:9)
When you know God through His son, Jesus Christ it is unimaginable to believe that He doesn't exist and so it is unimaginable to believe that there is an "acceptable reason for not believing in God." However I can certainly understand why some choose not to believe.