Question: "Does the Bible say 'come as you are'?"
Answer: While the concept of “come as you are,” if understood correctly, is biblical, the precise phrase “come as you are” is not found in Scripture. But, again, the Bible does have a variety of verses that imply the same message, based on God's amazing grace.
In Joel 2:32, where the prophet is declaring the terrible judgments of the Day of the Lord, God's offer of deliverance is open to “whosoever shall call upon the name of the Lord.” In Isaiah 1:18, God offers the invitation to come, though your sins are as scarlet, and He will make them white as snow. Revelation 22:17 is the invitation in the new Heaven, which says “Come! Whosoever will, let him take the water of life freely.” In these and other verses, the clear implication is that, even though we are sinners, God desires us to come to Him as we are, so that He can cleanse us.
As for the meaning and application of the phrase, we can go to the examples of how Jesus dealt with the sinners He encountered. Sometimes well-meaning Christians tell people that they have to “clean up their lives” before God will accept them, but that is not what we see in Scripture. When speaking to the woman at the well who was living with a man she was not married to (John 4:1-26), Jesus addressed the fact of her sin, then offered her the salvation she needed. Again, when the woman caught in adultery (John 8:1-11) was brought before Jesus, he told her “go, and sin no more.” The sin was never excused or ignored, but forgiveness was offered to anyone who recognized the truth of their sin and was willing to confess and forsake it. While God certainly expects us to leave our sin, that comes as a part of our salvation, not as a prerequisite. We are not able to clean ourselves up without God's help.
“Come as you are” is sometimes misunderstood and misapplied in today's church. Those churches which are identified with the Emerging/Emergent Church or Hipster movements, among others, sometimes take the grace of God and turn it into licentiousness (Jude 4) by teaching that it makes no difference how you live, as long as you believe. If you come to Christ in an illicit relationship, they say Christ will accept you just as you are and sanctify that relationship. If you come to Christ as someone who enjoys the night life, you can continue those things, and use them to “reach others for Christ.” This may be a popular message, but it directly contradicts Scripture which clearly says that these things from our past lives should be left behind and that our former friends will think us strange for doing so (1 Peter 4:3-4). Romans 13:13 commands us to walk honestly, or decently, no longer participating in the licentious lifestyle of the world. Galatians 5:13 says that we are called to liberty, but that we cannot use liberty “for an occasion to the flesh,” excusing our continued sins.
God is amazing, gracious, loving, and forgiving, so He calls us to salvation, even though we don't deserve it. While we were still sinners, Christ died for us (Romans 5:8), making it possible for us to receive forgiveness. He requires us to confess and forsake our sins when we come to Him, but He receives us just as we are, then begins to change us as we submit to Him in obedience.