This Table is a table of communion, and since it is offered to sinners, it presupposes forgiveness. But this has implications.
The Lord teaches us that we are to be reconciled to Him, and His forgiveness makes this possible. But He also teaches that, as far as it is possible with us, we are to be reconciled to one another.
Reconciliation with God through Christ is easy for us to understand theologically, for He is perfect. But how are we to be reconciled to fellow Christians, coming to this Table with us, when we believe (and perhaps believe heartily) that they are continuing to sin against us? They have failed to see the striking ways in which they have wronged us. Or perhaps they know they have wronged us, and have confessed it, but do not appear to know the extent of their iniquity? The answer is that we are to cover it in love, and recognize that to his own master he stands or falls.
Of course if it is not a matter of nuance, interpretation, he said, she said, but rather a matter of objective, verifiable sin, such a defiant sinner should be kept from the Table. That is what excommunication is for, but such things are applied to unrepentant adulterers, bank robbers, idolaters, and liars. It is not applied when someone sinfully rolls their eyes at you.
Related to this, when someone has sinned in a significant way, but has repented and been restored by the elders (whether you know all the facts or not), that is not a time to shrink back. This is fundamental: the forgiveness we have received is the same kind of forgiveness we are to extend. Refusal to forgive the repentant is nothing but moralistic Pharisaism.
Acceptance of someone back into fellowship is not to be confused with the disobedience (so common today) of letting disqualified leaders continue to serve in their offices. But neither do “standards” require us to shun those fellow sinners who have in fact put thing right. Not only is there fellowship at this Table, there is fellowship around this Table.
So come, and welcome, to Jesus Christ.