Ultimately, a person is a Christian if they are united to Christ by faith in His finished work on the cross. Romans 10:9-10 says, "If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved. " (NIV) This salvation is a free gift of God (Ephesians 2:8-9) and since it is essentially a work of God in your heart, it does not depend upon where you are, who you are, who you are related to, what church you go to or anything else. Salvation belongs to our God, and any lost sinner who puts his or her faith in Jesus will be saved.
Here are a handful of Bible passages that might help you to solidify in your mind what God has already guaranteed through Christ the cornerstone. 1 John 5:11-13; Romans 8:1; John 1:12; Romans 8:15-16. I would bet that there are countless other verses that would help.
Oh, two other thoughts - people will know that we are his disciples by our love for on another. (John 13:35) And I really liked SJmorningsun25's comment about a "crutch" - we all hobble into God's presence in our weakness and His strength.