The New Testament, as I understand it, only suggests two requirements for partaking of the Lord’s table:
(1) It is for believers, all members of the Body of Christ, not just a church member. All believers belong to His body. Partaking is a testimony of a person’s faith and continued fellowship with the Lord (1 Cor. 10:16-22; 11:17f).
(2) Believers should only partake if they are in fellowship or after careful examination of their attitudes and heart (1 Cor. 11:28f).
But this is presented as a personal thing, something that is left up to the individual to decide. The warning of 1 Corinthians is for individuals who are assembled and who, if they wrongly partake of the communion, could come under God’s judgment as explained in 1 Cor. 11:28f. Church leaders should explain the texts and give the warnings and time for personal examination before offering communion, but I do not see any justification for having mandatory restrictions established to prohibit people from taking part in communion.
Now, there are church discipline principles that govern fellowship with believers in rebellion, but that does not just apply to communion. In fact, communion is never mentioned. What is involved is a responsibility to avoid having intimate fellowship and going on as though nothing were wrong. Concerning such Paul reminds us:
2 Thessalonians 3:11-15 For we hear that some among you are leading an undisciplined life, doing no work at all, but acting like busybodies. Now such persons we command and exhort in the Lord Jesus Christ to work in quiet fashion and eat their own bread. But as for you, brethren, do not grow weary of doing good. And if anyone does not obey our instruction in this letter, take special note of that man and do not associate with him (intimate fellowship), so that he may be put to shame. And yet do not regard him as an enemy, but admonish him as a brother.
Some use of 2 Tim. 2:19f to support restricting believers from the Lord’s table, but that is really not Paul’s point in this passage and is a wrong application of the text. (Unfortunately, sometimes a lot of heresy is taught in the name of application.) The concern here regards false teachers and their influence on the church and particularly Timothy.
Timothy was to have nothing to do with the false teachers. In this way he would be a vessel: (1) “for noble purposes” (“unto honor,” timen), (2) made holy (“set apart”), (3) useful (“serviceable”) to the Master, and (4) prepared to do any good work (cf. 2 Tim. 3:16). What is clean and set apart for special use can easily get contaminated and be rendered unusable through contact with the corrupt. Paul was concerned that Timothy, his choicest disciple, keep himself in a usable condition for the Lord (John F. Walvoord, Roy B. Zuck, Editors, The Bible Knowledge Commentary, Victor Books, Wheaton, 1983,1985, electronic media).
Zondervan’s Expositors Bible Commentary says this:
On the basis of this (the statements about various vessels), as well as the context here in 2 Timothy, some scholars feel that the articles for ignoble purposes are the false teachers in the church (vv. 16-18), who are destined for eternal destruction. In that case, “if a man cleanses himself from the latter” (v. 21) means that Timothy must expel from the church the ignoble members.
Another interpretation is less drastic. It holds that in “a large house”—the visible church or a local congregation—there are members who are prepared for “noble purposes” and others who are fitted for more menial tasks. Both have their place and function in the church. Verse 21 would then mean that the individual who cleanses himself from “the latter” (touton, “these things,” perhaps false teachings) will be “an instrument for noble purposes” (skeuos eis timen). He will be “made holy” (hegiasmenon, “sanctified”), “useful to the Master” (euchreston to despote) “and prepared to do any good work.”
Both of these interpretations seem valid. Since we cannot be sure which one Paul had in mind, perhaps we should make both applications.