Only the unrepentant are unwelcome at the Lord’s Table. Those who will not believe in and submit to Jesus do not have any part of Him. Those who profess faith but undo their profession by ongoing rebellion to His commands are disciplined away from the fellowship of this meal. But every other believer is invited. More than that, every believer is being changed by it. Take, for example, those believers that Paul categorizes in 1 Thessalonians 5:14.
Christian, are you idle? Consider the humble and exhausting service of Your Lord. He labored in life up to and through death for you, and even now prays for You. Think of the work that went into this meal and get off your rear.
Christian, are you faint-hearted? Consider the resurrection of Your Lord. He died and was buried, but He rose again on the third day just as He promised so that you would have life (1 Thessalonians 5:10). His will cannot be stopped, and no one can stop Him from loving You. Think of the faithfulness and courage that this meal represents and don’t shrink back.
Christian, are you weak? Consider the nature of Your Lord. He does not break the bruised reed or quench the smoldering wick. He partook of the same things as you, He was tempted in all ways as you are, and so He sympathizes with your weaknesses (Hebrews 2:14; 4:15). Think of His tenderness, His gentleness, His kindness to you even in this meal. You are not solo in your need.
Whatever the problem, Jesus does not leave us where we are. He knows who needs to grow and what is lacking in their faith. He is patient, just as He calls us to be patient with one another. But He is always working toward His will that we all be completely sanctified even when we eat the bread and drink the cup of communion. No believer will be left behind.