One of the great games of LDS theology is to play "pin the tail on the church" and attempt to specifically correlate the text with an known institution. This is an idea with a long underground current.
Making a correlation between any church and the "great and abominable church" is no longer en vogue in official doctrine. Where Bruce R. McConkie might have declared it to be the Roman Catholic church in the first edition of Mormon Doctrine, subsequent editions take a more universal view of the nature of the "church of the devil".
"The titles church of the devil and great and abominable church are used to identify all churches or organizations of whatever name or nature -- whether political, philosophical, educational, economic social, fraternal, civic, or religious -- which are designed to take men on a course that leads away from God and his laws and thus from salvation in the kingdom of God." (Bruce R. McConkie, Mormon Doctrine, p.137 CHURCH OF THE DEVIL).
A more modern compilation of LDS information, including doctrinal positions, is found in the Encyclopedia of Mormonism. In that text, the definition is likewise universal rather than specific:
"The phrase "great and abominable church," which appears in an apocalyptic vision received by the Book of Mormon prophet Nephi in the sixth century B.C. (1 Ne. 13:6), refers to the church of the devil and is understood by Latter-day Saints to be equivalent to the "great whore that sitteth upon many waters" described in Revelation 17:1. This "whore of all the earth" is identified by Nephi's brother Jacob as all those who are against God and who fight against Zion, in all periods of time (2 Ne. 10:16). Nephi did not write a detailed account of everything he saw in the vision, as this responsibility was reserved for John the apostle, who was to receive the same vision; however, Nephi repeatedly refers to its content and teachings, using various images and phrases (1 Ne. 13:4-9, 26-27, 34; 14:1-4, 9-17)." (Encyclopedia of Mormonism, Vol.2, GREAT AND ABOMINABLE CHURCH).
That same source indicates that Nephi's words were not meant to define a particular organized entity: "When Nephi speaks typologically rather than historically, he identifies all the enemies of the Saints with the church of the devil (1 Ne. 14:9-10; 2 Ne. 10:16). They are those from all nations and all time periods who desire "to get gain, andpower over the flesh, andto become popular in the eyes of the world,who seek the lusts of the flesh and the things of the world, and to do all manner of iniquity" (1 Ne. 22:23)." (Encyclopedia of Mormonism, Vol.2, GREAT AND ABOMINABLE CHURCH).
Nevertheless, the pronouncements of the leaders of the church have not always been so ecumenical:
"The Lord has told us in the scriptures that in the last days there will be two churches. John the Revelator spoke of the great church with worldly power that had under its dominion and leadership the kings of the earth--he spoke of it as Babylon, the Mother of Harlots; and Nephi spoke of it as the great and abominable church. I am not going to say what that church is, though I have a very definite and clear idea. But I want to say that those scriptures also tell us that the other church is a weak church, a church to whose assistance God has to come in order to preserve it. We certainly are not the great church, for no kings are tied to the chariot wheels of our Church. We are the other church." (J. Reuben Clark, Jr., Conference Report, April 1949, p.162).
While Elder Clark might have a broad definition in mind, the implication is clear that he would identify one if pressed. Such reticence to name the church can easily be seen as attempt at a conciliatory presentation, when the private belief was to identify a particular location.
It might be tempting to ascribe this interpretation to the influence of early American anti-Catholic feeling. It is certain that this played a part in the individual interpretations of this passage, but cannot be used to define official belief. Indeed, there is good evidence that the more universal approach also had its adherents at an earlier time:
"Although the great "mother of abominations" has not gathered together in multitudes upon the face of the earth among all the nations and kingdoms of the Gentiles to fight against the Lamb of god and his Saints, yet there has been enough fulfilled to show that the balance will be accomplished. Has this great and abominable power, under the name of "the mother of harlots," popularly called Christendom, fought against the Saints in this country? Let the history of this Church answer that question; let the scenes we have passed through in the land of Missouri testify; let the tribulation this people had to endure in the state of Illinois bear witness. We will not refer to persecutions in Utah, for here we have had but little, compared with scenes we have past through in former years. Suffice it to say multitudes have been gathered together--under the influence of what? Under the influence of that great and abominable church or system called "the mother of harlots." (Journal of Discourses, Vol.7, p.184, Orson Pratt, July 10, 1859).
By focusing on the persecutions of the Saints, Orson Pratt must necessarily provide a greater context for the "great and abominable church" than a single organization, as the persecution against the Saints could never be seen as a Roman Catholic persecution. Orson Pratt is even more clear that he opens the interpretation to a larger spectrum:
"Since the Church with its authority and power has been caught away from the earth, the great mother of harlots with all her descendants has blasphemously assumed the authority of administering some of the sacred ordinances of the gospel. They have blasphemed the name of the Father, Son and Holy Ghost, by using it without authority in their ministrations. They have dishonored the name of Christ, by calling their powerless, apostate, filthy and most abominable churches, the Church of Christ. The whole Romish, Greek and Protestant ministry, from the pope down through every grade of office, are as destitute of authority from God, as the devil and his angels. The Almighty abhors all their wicked pretensions, as He does the very gates of hell. (Orson Pratt Divine Authenticity of BofM, No. 2 (1850), p.18 - p.19).
Elder Pratt opens up the "church of the devil" to all non-LDS Christian religions. Modern definitions have spread that idea even further. What can we say further about the "great and abominable church"?
In Nephi's vocabulary, the word "church" should be out of place. "Church" as a translation for the Greek "ecclesia" is a New Testament concept. The concept of an initiated and localized congregation is also post-New Testament in the Bible, with the Hebrew faith gathering in Synagogues, another inheritance from the Greek word which has the meaning of gathering together. The religious worship of the Hebrews would be difficult to shoehorn into our notion of a "church".
Nevertheless, Nephi is found using the word one time outside of the phraseology accompanying the "great and abominable church":
1 Nephi 4:26 "And he, supposing that I spake of the brethren of the church, and that I was truly that Laban whom I had slain, wherefore he did follow me."
This is ultimately a question of the nature of the translation of the Book of Mormon. Either the presence of the word "church" in this passage is a remnant of Joseph's hand in the translation, or Nephi is using a term which later becomes our "church" in a very different context. Certainly Nephi would understand the religious organization of his own time and land, and would not conflate what we would term synagogue and church.
This difference in understanding should underlie our perception of the "great and abominable church". In Nephi's terms and conceptions, he really had no ready label with which to classify what became the great churches. He must have meant something else.
The correlation of the "great and abominable" church with any particular institution should be seen as a culturally influenced attempt to make sense of this verse, and that past interpretations have fallen victim to cultural prejudices in naming that organization.
As an aside, it should be noted that there is a true "church" in the Book of Mormon prior to New Testament times, but this comes directly as a result of Alma's pioneering efforts, and is demonstrably a different organizational force than the communal religion practiced up to that time.