If hobgoblinism means the denial of any relevance for consistency -- as seems to be suggested by Schwyzer's comment that the word "foolish" in the quote is redundant -- it leads immediately to relativism. Rational argument works by demanding consistency between propositions, evidence, etc. So it's not surprising that few hobgoblinists (including Schwyzer himself in a later comment) would hold that hobgoblinism applies universally.
But if hobgoblinism's scope is limited, the critical question becomes defining its scope. What forms of consistency count as "foolish"? I have yet to find anyone even attempting to put some substance on that criterion (not even Emerson himself, as Bartleby's snarkily notes) -- either in terms of universal standards of foolishness, or in terms of why the specific consistency at issue is or is not a foolish one. Quoting the aphorism is treated as a final word. But without some specificity to the idea of foolish consistency, limited hobgoblinism collapses into universal hobgoblinism.
I do think there's a grain of truth to hobgoblinism. Truth must be consistent, and so inconsistency is always a marker that we don't quite have things right. But consistency need not be pursued at all costs. Consistency in one obvious context may force us into more significant inconsistencies somewhere else. There may be reasons we have not yet clarified that show why an apparent inconsistency is not actually inconsistent. We may have other good reasons to hold each of the inconsistent beliefs in their own domains. How a given inconsistency should be resolved may be unclear at the moment. In each of these cases, however, the acceptance of inconsistency is a provisional reservation of judgment, not a high-minded rejection of hobgoblins.
*My very least favorite is the Margaret Mead quote about small groups changing the world, which I think would make a good motto for al-Qaida.