Jürgen Moltmann says that Jesus Christ's invitation to the Lord's Supper extends beyond the frontier of Christianity and includes the whole world, such that atheists and non-Christians are invited to partake the Eucharist. Moltmann argues that no restrictions to the Lord's Supper are justified, because Jesus invited the tax-collectors and sinners first of all. Therefore Moltmann advocates for an Open Communion that is far more open that most churches allow because most churches restrict the Lord's Supper to only the members of their respective denomination. Moltmann responds that it is not his openness that must be justified, but all who fence the Lord's Table bear the burden of justifying their restrictions, especially since we are commanded not to break fellowship and not to cause divisions in the Church (c.f. 1 Cor 9-13).

Moltmann argues for a eucharistic community, which means that for reconciliation to occur, the unreconciled parties must first share a meal together, and afterwards they begin talking and the reconciliation process. Unless the invitation to the meal is offered first, then talking will never begin, and reconciliation will not occur. So not inviting the whole world, including atheist, non-Christians, sinners and tax-collectors to the Lord's Supper is prevent those people from coming to Jesus. Once they respond to the invitation, and they partake in the Lord's Supper, our eyes are opened to Jesus in the breaking of the bread (Luke 24:31).     

Moltmann's argument for an open communion and eucharistic community is his book The Church in the Power of the Spirit: A Contribution to Messianic Ecclesiology.

Moltmann writes "The Lord's supper takes place on the basis of an invitation which is as open as the outstretched arms of Christ on the cross. Because he died for the reconciliation of 'the world', the world is invited to reconciliation in the supper. It is not the openness of this invitation, it is the restrictive measures of the church which have to be justified before the face of the crucified Jesus. But which of us can justify them in his sight? the openness of the crucified Lord's invitation to his supper and his fellowship reaches beyond the frontiers of the different denominations. It even reaches beyond the frontiers of Christianity; for it is addressed to 'all nations' and to 'tax-collectors and sinners' first of all. Consequently we understand Christ's invitation as being open, not merely to the churches but to the whole world." [1]

Jürgen Moltmann also explained his eucharistic community at the 2009 Emergent Village Theological Conversation. I've included an audio clip from session six, and transcribed it:

Moltmann said "We do not celebrate on the Lord's Table our theories about his presence, but his presence. We may have different theories about how in what way He is present, but let us celebrate his presence first, and after eating and drinking on the Lord's Table, let us sit together and talk about our different theories. If we start without different theories, we would never come to the table and would never come to an end. After eating and drinking, every dialog is better than with thirty throats and an empty stomach. Therefore, I go to every invitation where I hear the inviting words of Christ, whether this is a Catholic church, or Orthodox church, or any denomination—I don't care. So far, no priest has said 'you are not invited, only those who belong to our denomination are invited.'  Jesus invited all those who are weary and burdened to come to Him. He is not inviting Catholics only, or Presbyterians only, or Methodists only: this would not be the Jesus I know." [2]

Sources:

1. Jürgen Moltmann, The Church in the Power of the Spirit: A Contribution to Messianic Ecclesiology. p. 246. 
2. Jürgen Moltmann at the 2009 Emergent Village Theological Conversation, Session 6 starting at 49mins, trans. Wyatt Houtz [Used with permission]  
3. Header Image: source wikipedia