Romans 15:7 NKJV - "Therefore receive one another, just as Christ also received us, to the glory of God."
This has spoken to my heart so many times when I think of how God accepted me, "warts and all!" He loved me and basically told me to come, "Just As I Am" like the old invitational hymn said. He didn't make me change myself - He would do all the changing when I became His child. I am a new creation!
And if God accepted me like that and He accepts every sinner like that, then why should I not receive every believing sinner like God does?! We older Christians need to recognize that our treatment of new believers gives them a personal understanding of God's love for them. As we love them we show them the love of Christ. It's just like showing love to your baby - as that child grows and you begin to talk with them about God's love they associate that thought with the way they feel when you love them. And "babes in Christ" do the same thing. Our acceptance of new believers gives them such a sense of security and welcome in the family of God.
I don't want to dwell on the negative side of this too much but I'm sure we've all felt the "distance" some Christians have shown us. Many new believers have felt an estrangement from God because of how they were treated by older believers who should have known better. The next time you meet a believer, whether a new child of the kingdom or an older Christian, show them acceptance as you know God accepts you.