Should everyone read the whole bible?

This question first entered my mind last week when, in a meeting, someone compared being wishy-washy at work to what Jesus says in Revelation about the church at Laodicea: "So, because you are lukewarm—neither hot nor cold—I am about to spit you out of my mouth." -Revelation 3:16. Now, this is an important verse, and is instructinoal to followers of Christ. But, it may not be useful to bring up in a room full of people who don't know Christ.

Then, last night during my devotional time, I read this:
"I, Simon Peter, am a servant and apostle of Jesus Christ. I write this to you whose experience with God is as life-changing as ours, all due to our God's straight dealing and the intervention of our God and Savior, Jesus Christ." -2 Peter 1:1 (The Message)

This got me thinking- Peter wrote this letter to believers. Should we encourage non-believers to read it? If they do, will they get it? Should non-believers read Leviticus before they understand how it relates to the grace offered through the life and death of Jesus Christ? Would it be helpful or hurtful?

Don't get me wrong- I know "All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness." But is all scripture useful to all people at all points on their faith journey? As Christ followers/ teachers/ shepherds, is part of our responsibility to point people to the right parts of scripture for their level of understanding and belief?

Just something I've struggled with lately. Feel free to weigh in.