The Church (The body of Christ made up of his followers who have been saved by Grace) is first for the believer. The gathering of the church is of course welcome to non-believers so that they can potentially receive the gospel, be exposed to (hopefully) the loving nature of the family of God, to see and to hear God's call to salvation. Inviting a non-believer to church is a common method of evangelism. But as with all evangelistic efforts, it must be guided by the spirit. Sometimes a non-believer going to church with their believing friend is a bad idea.
The situation all depends on the prompting of the Holy Spirit. I Corinthians 12 and 14 talk about the role of the body of Christ and how to present their spiritual gifts. I believe it is acceptable for a non-believer to go. What a bad example it would be if someone stopped a non-believer, who comes to church of their own volition seeking truth, and told them they were not welcome due to lack of membership.