Should non-believers be allowed in church?

The church is a gathering of BELIEVERS. It's meant to be a place where Christians gather to be re-energized so they can go back out into the world. In the beginning, the deal was that an individual believer has the responsibility to evangelize. Once that soul or nonbeliever accepts Christ, then he or she should be invited into the church. We weren't meant to go out, grab a few unbelievers and bring them to our pastor to evangelize. The layman has forfeited his original design. That's why pastors have resorted to telling their people to invite friends and neighbors to church. The danger comes in when these unbelievers become leaders or influence the church in ways that cause the church to become liberal in their thinking. I always ask - how do you know you'll change them before they change you? Paul tells us not to be yoked together with unbelievers. Why? Because bad company corrupts. This is why church should be for believers, not non-believers.

There's a place for open groups and closed groups. John Wesley of the Methodist movement had the small groups open and the large groups closed. You had to get a ticket in a small group to enter the large group! Small groups are for personal ministry; large groups are for teaching, just like in Acts 2. No anonymity here.

I agree with the idea of unbelievers not participating in Holy Communcion, but seekers should be permitted among the congregation if they do not distract--i.e. are truly seeking:

From 1 Corinthians 14

23 So if the whole church comes together and everyone speaks in tongues, and inquirers or unbelievers come in, will they not say that you are out of your mind? 24 But if an unbeliever or an inquirer comes in while everyone is prophesying, they are convicted of sin and are brought under judgment by all, 25 as the secrets of their hearts are laid bare. So they will fall down and worship God, exclaiming, “God is really among you!”

Paul, in 1st Corinthians chapter 5 and the third chapters in Titus and in 2nd Thessalonians, mentions disassociation with disruptive and/or lazy so-called believers and/or believers that are "sexually immoral or greedy, an idolater or slanderer, a drunkard or swindler. Do not even eat with such people." but this is a church discipline issue. if we're not careful, the church can be severely corrupted if it does not take a tangible stand on moral issues. this can destroy a church if it is not vigilant about such internal corruption.

and there are certain church meetings where it might be expected that they are restricted to church members only. meetings like church discipline of erring members, or meetings where salient church vision and positions are discussed and decided. some churches might want to restrict the Lord's Supper to their intimate members.

but there is no good reason to exclude non-believers from the dissemination of the gospel (hearing the Message) nor from worship as long as they have enough respect to behave themselves (anyone who is disruptive may be asked to leave and be literally shown the door if they don't "get it"). in Mark chapter 2, Jesus said "It is not the healthy who need a doctor, but the sick. I have not come to call the righteous, but sinners."

This is also the case among the Eastern Orthodox - if you're not Orthodox you get as far as the narthex but no further. Their practice is not based solely on scripture, but also on tradition. The basic idea is that the Church is unified as the Body of Christ, and this unity is expressed and sanctified by common participation in the Eucharist; it is therefore wrong to allow people who are not part of the Church to take part in the service. It is a more extreme version than, say, the Catholic position that you can be physically present in the church building, but not go up to receive the sacrament.

Scriptural support for unity through the Eucharist is found principally in 1 Corinthians 10-12 and in John 6:25-59, though there are other passages (like Acts 2:42-47) that speak about unity of the community of believers in a general way.

Is not the cup of thanksgiving for which we give thanks a participation in the blood of Christ? And is not the bread that we break a participation in the body of Christ? Because there is one loaf, we, who are many, are one body, for we all share the one loaf. (1 Cor 10:16-17, NIV)

The inference is that believers are united, but believers+unbelievers are not, and so there is no true koinonia ("participation" above, also translatable as "fellowship" or "community") if the celebration of the Eucharist does not reflect the unity of Church membership.