In the name of keeping the ungodly and rebellious away from the Table, many well-intentioned Christians have only succeeded in keeping the tender-hearted away. It is analogous to the bumpersticker that says when guns are outlawed, only outlaws will have guns. When the hard-hearted are whacked, only the tender-hearted listen.
When warnings are given to you to police yourselves in how you come to the Table, the result is that those who are willing to do so assume the responsibility of it, and those who do not care to bother themselves continue to come. This is why we urge you to come to the Table if you are a baptized member of God’s covenant household. Examining yourself does not mean excommunicating yourself. So in fact, you must come.
When the Table is honored in this way, and when the Word accompanies it rightly, those who are continuing to come even though they are engaged in secret hypocrisy are doing no harm to the Table. The Table is not threatened by sin anymore than an extremely potent herbicide is threatened by weeds in a field. We don’t need to protect the Supper. We fence the Supper for the sake of those who would mock God, and not because we are fearful that the Supper of God will somehow be damaged.
If you are under lawful discipline, then you should not come. If you have sinned, but are not under discipline, then you should have confessed that sin at the beginning of the service, and you should come now. If you neglected to confess it then, then confess it now, and come. If it is significant sin, requiring significant restitution, then confess it, come to the Table, seeking strength to do what you know you have to do. In short, you ought not to be suspending yourself from the Supper—you do not have that authority.
You are quite right that sin and the Supper do not go together. But to resolve this tension, you must give up the sin. Not the Supper.