1 Tim. 4:1 is a well recognized by LDS as a scripture prophesying the apostasy of the early Christian Church. I’ve compiled a few commentaries on this passage from Protestants and LDS alike:
They will apostatize from the faith, i.e. from Christianity; renouncing the whole system in effect, by bringing in doctrines which render its essential truths null and void, or denying and renouncing such doctrines as are essential to Christianity as a system of salvation. A man may hold all the truths of Christianity, and yet render them of none effect by holding other doctrines which counteract their influence; or he may apostatize by denying some essential doctrine, though he bring in nothing heterodox (Adam Clarke. Commentary on the Bible).
The Greek word here – apostesontai – is that from which we have derived the word “apostatize,” and would be properly so rendered here. The meaning is, that they would “apostatize” from the belief of the truths of the gospel. It does not mean that, as individuals, they would have been true Christians; but that there would be a departure from the great doctrines which constitute the Christian faith. The ways in which they would do this are immediately specified, showing what the apostle meant here by departing from the faith. They would give heed to seducing spirits, to the doctrines of devils, etc. The use of the word “some” does not imply that the number would be small. The meaning is, that “certain persons” would thus depart, or that “there would be” an apostasy of the kind here mentioned, in the last days. From the parallel passage in 2 Th. 2:3, it would seem that this was to be an extensive apostasy (Albert Barnes [1798-1870] Notes on the Bible).
In Paul’s first letter to Timothy, he prophesied concerning the departure of some of the saints from the faith…This prophecy has a number of features that make it of considerable interest. First of all, Paul specifically stated that his belief in the future defection was the result of revelation. In fact, not only did the Spirit speak these words to Paul, but it did so “expressly.” The chronological note is also important. Paul used the term “latter times” (hú fneroi kairoí) to denote the period in which the developments that he foretold would take place. In the ultimate sense, the period of time in which we now live can be called “the latter times” better than any other. As we learn through modern revelation, our day is the dispensation of the fulness of times — the preparatory era that precedes the Second Coming of the Savior. Yet Paul spoke using a different definition for “latter times.” His focus was on the last days of the Christianity of his era, the “latter times” of the early church.
A few decades after Paul foretold the departure of some from the faith in the “latter times,” Jude announced to his readers that they were then in “the last time” (é fnhatos chrs, Jude 1:17-19). Similarly, John expressed to the readers of his first letter the certainty of the fact that they themselves were in “the last hour” (escháebar; hoabar;, 1 John 2:18-19). With the revealed knowledge of important future events, John and Jude knew that they were not in the final era of the world. But their words reveal the fact that they knew that they were in the final days of the Christian church. That was the period of time concerning which the spirit spoke “expressly” (1 Timothy 4:1) to Paul.
…[T]he departure from the faith would be a rebellion against true principles of doctrine. Paul wrote that those who would depart would give heed to what he calls “seducing spirits” and “doctrines of devils.” It must be emphasized that what Paul saw was not an abandonment of religion but a shifting of loyalties from “the faith” to a false faith. Accompanying this defection would be the manifestation of the negative character traits cited in 1 Timothy 4:2.
1 Timothy 4:3 is interesting because it mentions two examples of the false ideas that the counterfeit religious system would foster: a prohibition against marriage and a prohibition against certain foods. Beyond that the Apostle gave no further details (Kent P. Jackson in John M. Lundquist and Stephen D. Ricks, eds., By Study and Also by Faith, 1: 89).