You remember the story of the conversion of Saul of Tarsus. He was a persecuter of the church. He was "breathing threats and murder against the disciples of the Lord" (Acts 9:1) and set out with permission to hunt down anyone "belonging to the Way" (Acts 9:2). Traveling to Damascus to persecute the church there, he ran into an unexpected person -- the person of the Resurrected Christ. There, on the ground, he heard, "Saul, Saul, why are you persecuting Me?" (Acts 9:4) Oh, now, hold on. I think Jesus made a mistake there, didn't He? I mean, the text was clear. Saul wasn't persecuting Christ; he was hounding Christians. It was the church he was after. If that was your objection, I point to this text to help us see that Scripture connects Christ and the Church. Scripture, in fact, refers to the Church as "the Body of Christ" (Eph 4:12).
Given this fact, how is it that genuine Christians might not be part of a church? Isn't that a Christian not being part of Christ?
In his first epistle to the church at Corinthians, Paul really draws a pretty picture. I won't quote it all. You know how it goes. But he gives us two types of irrational viewpoints. On one side, you have the "They don't need me" view, and on the other the "I don't need you" view. He starts with the claim that all believers are part of the body (1 Cor 12:12). Then he writes about a crazy foot. "If the foot says, 'Because I am not a hand, I am not a part of the body,' it is not for this reason any the less a part of the body." (1 Cor 12:15) This foot is thinking, "Because I'm not a 'useful' part of the body (by some strange evaluation of 'useful'), I'm not needed." And Paul says that's stinkin' thinkin'. Then there is the other side. "And the eye cannot say to the hand, 'I have no need of you'; or again the head to the feet, 'I have no need of you.'" (1 Cor 12:21) No one can tell any believer, "We don't need you." Paul's point here is that each member of the Body of Christ is important. "To each one is given the manifestation of the Spirit for the common good." (1 Cor 12:7) Do you see what he's saying? The church needs each one of us, and each one of us needs the church.
And still we have many people who 1) call themselves Christians and 2) are not involved in the Body of Christ. They aren't exercising their gifts. They aren't ministering to fellow believers. They aren't building up the saints. They find this whole "organized religion" thing a bit tedious, or they complain about "hypocrites in the church", or they just can't find a church that "suits my needs". You can point out that there isn't a biblical paradigm for believers that includes not being part of a local body. They shrug. You can show them verses that tell us to not forsake assembling together (Heb 10:25), and they smile and say, "No, thanks; I'm fine." You can point out Jesus's basic command for us to love one another (John 13:34) and point out that Jesus said it was the hallmark of a Christian (John 13:35), and they'll still pass. They're passing in growing numbers.
There are lots of reasons Christians give for not being part of a local group of believers. Given what the Bible says about Christians and the church, it seems to me like an evisceration, like vivisection. The body is alive, but some of our body parts are rolling around on the floor, being neither productive nor cared for. There's a loose eye rolling around over there and a hand crawling about over here telling us, "Oh, don't mind me, I'm worshiping God in my own way." As if that makes any sense. John Aloisi of the Detroit Baptist Theological Seminary considers unchurched Christians "mythical beasts". I prefer to think of them as uninformed or unclear on the matter and in need of teaching, correction, reproof, and training in righteousness (2 Tim 3:16-17)... which they can get in any decent Bible-preaching church.