Who may partake communion/the Lord's Supper in a Baptist church? What shall we call the various views defining who can partake? A popular illustration in our area is that of a door -- it is either open or closed. There is actually some merit in that idea, but the definitions given by those who use the illustration often do not fit standard Baptist usage. In actual use, it is often a pejorative measure used to say that all communion that is not local-church-only is open communion.
There is a lot of baggage and misinformation surrounding the Lord's Supper. Part of the baggage is the use of terms that may mean different things to different people. Therefore, I prefer to usually speak in terms of unrestricted and restricted communion rather than open, close and closed. Open is fairly well-defined in both current and past usage, but there is little or no truly "open" communion. All the common Baptist versions of communion are "open" to some and "closed" to others. The issue is not whether the participants are restricted, but to what extent.
Below I will attempt some definitions. I must give credit to Nathan Finn and his blog post The Relationship between Baptism and the Lord’s Supper: Four Views. I had not heard of "modified" open communion before reading his post. I didn't see any reason to "reinvent the wheel", so the definitions 1, 2, 3, & 5 under "Restricted communion" are Nathan's definitions (though 1, 3, & 5 are slightly abridged and I've substituted my terminology in # 3).
Related to participants, there are two basic types of communion, restricted and unrestricted.
I. Unrestricted communion (Unrestricted means there are no restrictions on who may participate in communion.)
Theoretical unrestricted communion is the belief that there are absolutely no restrictions placed on who can take communion. It is seldom (if ever?) advocated in theory -- since Baptists and other denominations acknowledge that the Lord's Supper is for God's people and at least ideally restricted to them. Theoretical unrestricted communion, in practice, would be the active solicitation of other religions and even the non-religious to participate. Perhaps Universalists would be amenable to such practice. I do not know.
Practical unrestricted communion is the practice in which the elements of bread and wine are offered to all, putting the onus of participation entirely on the communicant. In theory, the church may hold that communion is intended for Christians only, but in practice no one is excluded or advised not to partake communion. This is practiced by Campbell/Restoration Movement churches in our area, and it may be practiced by some Baptists.
II. Restricted communion (Restricted means there are some restrictions on the participants in communion; that is, requirements that must be met before one participates in communion -- salvation, baptism, church membership, godly walk, or some combination of the foregoing prerequisites.)
Open communion is the belief that any professing Christian participate in the Lord’s Supper. (Nathan Finn)
“Modified” open communion is the belief that any professing Christian who has undergone some type of ceremony called “baptism” (regardless of mode) may participate in communion. This is often called open communion, but it is not as loose as true open communion. (Nathan Finn) [David Rogers further explains his view on this in the comments section and on his blog; David's view allows infant baptism to meet this standard for communion purposes, but not for actual baptism. This view in a sense makes baptism a prerequisite to communion, but then allows participation to anyone who feels he or she has been obedient to the Lord’s command for baptism. Therefore, in spirit it stands closer to "open" communion that strict/close/closed communion].
"Baptism-prerequisite" communion is the belief that any Christian who has been biblically baptized can participate in communion [or, put another way, that a valid baptism by immersion is a prerequisite to partaking of the Lord’s Supper; rlv]. Biblical baptism often includes the proper administrator (a baptistic church), the proper mode (immersion), the proper candidate (a believer) and the proper reason (symbolic of union with Christ rather than sacramentalism or baptismal regeneration). This practice has been variously called close, closed, restricted, and strict communion in Baptist history. (Nathan Finn) [In Baptism as a prerequisite to the Lord’s Supper, Nathan calls this view "Consistent communion" (rather than closed/strict), because Baptists "do not like to think of following biblical precedent as a negative act..." This "consistency" can be seen in contrast to the "modified-open" view -- baptism is the same in both cases as opposed to "modified-open" recognizing baptism as one thing for obedience to baptism and as something else for the purpose of communion. Note also that participants in "baptism as a prerequisite" communion may vary quite a bit based on whether a church believes all immersions should be performed by a Baptist administrator, or whether an immersion by an evangelical non-Baptist administrator is valid.]
Correspondence-only communion is the belief that communion should be restricted to baptized church members who are of "like faith and order". This is most obvious in Baptist churches that do not cooperate beyond the local association level, but create a "chain of correspondence" with other associations of "like faith and order" in order to maintain cooperation and fellowship. Members of churches within this associational chain of correspondence may commune together, but not those outside of it.
Local-church-only communion is the belief that communion should be restricted to members of the local church that is administering the ordinance, typically for reasons related to discipline and accountability. It became popular among 20th century historians to call this practice “closed” communion, but that is not entirely historically accurate. Historically, “closed” was used interchangeably with all the terms listed above. There is no official name for this practice; it is simply the most restrictive form of closed/close/strict/restricted communion, and many contemporary historians (myself included) simply call it local-church only communion. (Nathan Finn)
Note: This might interest some of you. I just read about Spurgeon's "modified/mixed open" communion: "Spurgeon’s attitude towards these questions has very often been misunderstood. He did not absolutely agree with the practice of the American Baptists regarding the communion, but he did very nearly, and it is an abuse of terms to call him an 'open communionist'. He did not advocate or practise the promiscuous invitation of all Christians to the table of the Lord. The communion service was held on Sunday afternoon in the Tabernacle, and admission was by ticket only. Members of the church, of course, were furnished with tickets. Any person not a member, desiring to attend and partake of the Supper, must satisfy the pastor or deacons that he was a member in good standing of an evangelical church, when he would receive a ticket. At the end of three months he would be quietly told that he had had an opportunity to become acquainted with the church, and they would be glad to have him present himself as a candidate for membership; otherwise he would do well to go elsewhere, where he could conscientiously unite." -- Vedder's Short History of the Baptists, Chapter 17