In a recent Out of Ur Blog, JI Packer weighed in on whether communion is open or not. Here are the first bits and I’m curious as to what you think. (The rest of his piece is at that link.)

Do you believe that access to the Lord’s Table should be
restricted, and if so, how does the church do that in a way that’s
inoffensive? [I would add this: If you were the person distributing the bread or wine, would you pass someone by or would you let them make the decision? If you were the one teaching, would you say this is open to anyone, to Christians only, or to seekers as well? How would you discriminate between folks? JI Packer answers as follows … do you agree with him or not?]

Yes, I believe access should be restricted at two points. First, the
folk who come to share the Lord’s Supper with the congregation should
be people who have shown that they can discern the Lord’s body. In
other words, they understand what the Communion service is all about:
Christ crucified for us.

The second point of restriction is when individuals in the
congregation are known to be living in sin. If the attempt has been
made to wean them away from sin according to the rules of Matthew 18,
and it’s failed, then the text says, “Let him be to you as a heathen
and a publican,” a tax collector, someone beyond the pale. The pastor,
with the backing of those who were trying to wean the person away,
should say, “Don’t come to the Lord’s Table. If you come, the bread and
wine will not be served to you. I shall see to that.”