For Whom Does the Church Exist?

Calvary Church, Stonington, CT

Yesterday afternoon, while talking to a Christian homeschooling parent about whether our struggling support group should remain exclusive (i.e., admit only those who agree with a statement of faith) or whether we should make it more accessible to all homeschoolers, I encountered this, which is not a direct quote:

Would you let unbelievers into your church where they can influence others with their non-Christian ideas?

As a practicing Lutheran, I was so astonished by this question, I could not think of a response.  Why?  Because one of the strategies for evangelism in my denomination is to bring people to church where they can hear the Word of God preached and taught.  An even better situation:  someone willingly enters the church because they are seeking God.  In this latter case, no one had to do any work to get them there;  they arrived on their own.  Why, then, would I turn them away, or prevent them from entering in the first place?  At that point, they are fair game for the unfettered teaching and preaching of the Word because, forgive the analogy, like prey in a spider web, they trapped themselves.

Which brings me to my question:  for whom does the church exist?  Is it only for those of us who already profess faith in Christ?  Or is it for believer and unbeliever alike, the believer to teach and witness and the unbeliever to learn and come to faith?  The former implies that the church is the body of believers and the Church is exclusively for those people, which makes me wonder about the importance of the Great Commission.  The latter, on the other hand, recognizes that the church is the body of believers and the Church has the job of evangelizing both within it's walls and without.

Can someone please explain this to me?!  I thought church and Church were about loving God and loving your neighbor.