Who can or should participate in Lord's Supper?

Gordon posted on Sola Panel about his thoughts on who should be allowed to participate in Lord's Supper. I have posted my response as a comment, although it was a bit long and might have been better to respond it here. I reproduce my response here nevertheless.

I think having a full meal seems more consistent to the Biblical description of Lord's Supper, somewhat like what you have described in your last paragraph.

But I am not so certain about the idea of extending the invitation to participate in the Lord's Supper to unbelievers (incidentally, I come from a denomination that has the same tradition on the issue). On one hand, I agree with what you said here. Seeing how Jesus dealt with sinners, and also as the Lord's Supper being a symbolic proclamation of the Gospel, it seems we actually should invite the unbelievers to participate. But, I think there's more to think through about the Lord's Supper.

Firstly, I am not sure if the meals Jesus shared with sinners were the same as when Jesus explicitly told His disciples about the Lord's Supper. Having fellowship with and not becoming segregated from sinners (but not all sinners to be sure, since Paul tells us to not even associate with a certain kinds of sinners, and Jesus also did not associate with all types of sinners all the time) is, I think, important and what Christians should be doing. But I think we should be careful when/if we extend the invitation to all, because the Gospel must be displayed clearly even as to discern and divide the hearts of men just like when we preach the Gospel with our mouths.

To illustrate this, I can think of baptism. Just like a man who was baptised without proper understanding of the Gospel may go on living in a false assurance of salvation, relying on the fact that he is baptised, rather than on the work of Christ, unbelievers who come to share in the Lord's Supper may go on living in their unbelief having a wrong sense and view of salvation, thinking that they are saved because they participate in church's sacraments.

This confusion may not have set in the lives and faith of early Christians, because when they did get baptised, and shared in Lord's Supper, they did so in the face of a real and visible persecution. The threat and danger that they'd have to face as a result of joining the Christian sect was clearly seen by a potential believer. So people who did not have the real conviction, wouldn't have risked it. But in this society where tolerance and relativism has deeply affected people's minds, when we let unbelievers to participate in the Lord's Supper, they may simply take it as an insurance for their ticket to heaven, and not because they are compelled and captivated by our Redeemer.

Of course, one may say that, we run this risk all the time. I think we do too. Whenever we meet at church, whenever we participate in ministry, we are running the risk of giving others and ourselves a false sense of security about salvation. But there are different degrees of the risk (as far as human responsibility goes under God's sovereignty), and the ministers and preachers of churches and ministries will have to gauge this risk carefully before making any drastic changes.