Is Communion for Christians Only?

A few weeks ago, I visited a church where this sign was displayed during communion. The method of serving was passing a tray through the aisle and taking a piece of bread and a small cup of juice, so it would not have been obvious if one chose not to partake.

United Methodists practice open communion, which to clarify, means that you do not have to be a member of the church where communion is being served or a member of any United Methodist Church to receive the sacrament.

This is different than saying that you have to be a Christian to receive, which is clearly what the church that I visited was indicating.

The official document on baptism for The United Methodist Church, By Water & The Spirit, indicates:

In celebrating the Eucharist, we remember the grace given to us in our baptism and partake of the spiritual food necessary for sustaining and fulfilling the promises of salvation. Because the table at which we gather belongs to the Lord, it should be open to all who respond to Christ’s love, regardless of age or church membership. The Wesleyan tradition has always recognized that Holy Communion may be an occasion for the reception of converting, justifying, and sanctifying grace. Unbaptized persons who receive communion should be counseled and nurtured toward baptism as soon as possible.

That last sentence is particularly tricky in practice. Do you ask people if they have been baptized before, during or after they receive the bread and the cup? Perhaps a message of this sort in a United Methodist Church would say:

If Jesus is lord of your life, please take communion. If he is not lord of your life, go ahead and take communion anyway, as you might experience a desire to make him the lord of your life, in which case we would like for you to be baptized if you haven't already been baptized.

This is a little tongue in cheek, however I do wonder - How does your church communicate about who receives Holy Communion?