To summarize what I've seen so far: Virtually all Baptists from John Smythe through the end of the seventeenth century held a strict view of church validity. They spoke liberally about false churches, readily identified which churches were indeed false, and generally included most churches other than their own within that number. Indeed, this was part of the way that they justified their existence. Some early Baptist writings state plainly enough that if there were another valid church, Baptists would be duty-bound to unite with it rather than to pursue their separate existence. As a side note, it is interesting to me to see this similarity of thought between early Baptists and the modern ecumenical movement—early Baptists apparently believed that some sort of organizational union among all true churches was necessary; they just didn't think that there were any other true churches with which they could unite.
In the earliest stages of Baptist development, we emphasized a number of deficiencies that would invalidate a church, listing the many points of difference between ourselves and other churches. By the middle of the eighteenth century, Baptist teaching seemed to have found two foci for attacks against the false churches: infant baptism and religious persecution. For example, in John Gill's exposition of Deuteronomy 32:32 he highlights persecution as that which invalidates false churches.
The tone of Baptist apologetics changed somewhat in the last half of the eighteenth century. References to the "false church" vis-a-vis the "true church" abated in Baptist literature. I think the primary cause is a spiritual awakening that touched two continents.
The Great AwakeningsThe First Great Awakening prompted some Baptists to rethink their ideas about church invalidity for several reasons. First, the Baptists by then had a century and a half of their own history to explain, and it posed its own blemishes. General Baptists had almost entirely fallen into Unitarianism. Particular Baptists had wandered through hyperCalvinism into antinomianism far too much. So, of the two main branches of Baptist life, one had forsaken God for a man-made theory of God, and the other had abandoned the pursuit of personal holiness and congregational discipline. Was this the one-and-only true church?
Second, Baptist recovery from these errors had to come by the hand of non-Baptist influences. Andrew Fuller rescued Baptist Calvinism from hyperCalvinism and antinomianism, but few of Fuller's ideas were original. Fuller avidly read Jonathan Edwards, and I think it perfectly fair to credit Edwards as much as anyone for the Particular Baptist recovery. General Baptists found deliverance in the person of Dan Taylor. The Methodists—members of the false Anglican church!—had won and trained Taylor. Across the Atlantic, American Baptists were being invigorated by nouveau Baptistes like Isaac Backus. Pro-revival Baptists admired and read revival leaders like Whitefield, Tennant, Frelinghuysen, and Edwards...none of whom were Baptists. Every one of these men served at pedobaptist churches. Was it logical to conclude that the false churches had been the salvation of the true churches?
Don't get me wrong: Baptists didn't recant the idea of the Great Apostasy; they just talked about it a lot less. Also, their theological conclusions about ecclesiology reflected some confusion during the eighteenth century. For example, the Philadelphia Baptist Association at various points throughout the century declared null-and-void any baptism performed by an improper administrator, proscribed Baptist member congregations from allowing preachers from other denominations to preach in their churches, and yet affirmed the validity of immersion performed by an Anglican priest.
During the Second Great Awakening, one major additional development took place. That development was Alexander Campbell. Campbell borrowed significantly from Baptist theology to create his restoration movement, but the Campbellites added their own twist to things. While retaining immersion, they abandoned the Baptist teaching about the meaning of baptism, returning to the Roman Catholic notion of baptismal regeneration. Most importantly, they claimed that Baptists were a false church. The Campbellites did not baptize infants and fully supported religious liberty. Thus, in one fell swoop, they re-ratcheted the level of rhetoric back to accusations of church invalidity and evaded the two most recent foci of Baptist teaching about false churches.
Thus ended a kinder, gentler era of Baptist rhetoric in America.