Now, Lindir is perhaps correct in assuming that a shepherd can differentiate between different sheep. His metaphor is referring to a shepherd being able to distinguish between men and hobbits, who are both mortal (not between, "mortal, and not a mortal' which is what you say).
Having read your post I first wondered how you could have misunderstood my post so much and now I see I forgot an "S" in there. What I meant to say was that "SOMEONE WHO KNOWS THE DIFFERENCE BETWEEN MORTAL
S AND IS NOT A MORTAL IS A SHEPHERD". So no, we are in complete agreement here - a shepherd is meant here as someone who knows the difference between mortals. And there is a second part to my phrase (which you misunderstood): "[a shepherd] is not mortal [himself]".
Now most of your explanation is sadly for nothing, because it relies on a misreading of my text due to a typo
so I will resume my rebuttal from the point which doesn't concern it.
Lindir's metaphor also mentions 'shepherds'. This implies the possibility that there are 'shepherds' who look after mortals. It also implies that Elves are not such shepherds. This also brings up the questions: Are there 'shepherds' who look after mortals in Middle Earth? Who are they? Should Elves be 'shepherds', and be looking after mortals? Are there 'shepherds' who look after Elves? (We already have enough evidence to guess that Elbereth and the Elder King might be 'shepherds' to Elves).
Once again, we are in complete agreement here. Yes, shepherds look after mortals, yes we can presumably construct something like this:
shepherds are to mortals
as
Elberth and the Elder King are to Elves
This, once again proves to me that Lindir was talking about the Istari, or more precisely, about the Istar present in Rivendell at this moment - Gandalf.
However, given Tolkien's letter to Robert Murray SJ. (letter 142), "The Lord of the Rings is of course a fundamentally religious and Catholic work: unconsciously so at first, but consciously in the revision," then, of course, we should always be ready for Catholic or Biblical references, especially in passages we know (like this one) to have been revised. (I would go so far as to venture a guess that this exact revision might well have been foremost in Tolkien's mind as he wrote that letter!)
Of course we cannot 'establish' that Lindir's 'sheep and shepherds' metaphor is a Biblical reference. We can, however, assume that it is very likely to be one.
The impact, if it is a Biblical reference, is just to emphasize, and call attention to all the questions which could have quite legitimately sprung to our minds on reading this passage even if there were no mention of 'sheep and shepherds' in the Bible. (Or, if Lindir's metaphor had been of 'cattle and cowboys'. By the way, the pre-revision metaphor was 'big peas and little peas', with no mention of 'gardeners', so, if we knew the revision history [which, we wouldn't, as first time readers], the inclusion of 'shepherds' alone should peak our interest in the questions implicit in the metaphor.)
Here we start to disagree because while I totally agree that LOTR is meant to be Catholic work (whatever that term might precisely mean - I remember
a great academic conference about precisely that topic that I took part in several years ago which still ended up with basically a lot of disparate ideas about how to understand that), I don't think that this passage was revised with any precise Biblical passage in mind. Yes, the basic idea (of a higher being acting as a shepherd to a lower being) is without a doubt a Biblical one but what I disagree with, is seeing a precise Biblical reference in it. And thus here we come to the last part of your post:
Biblical references don't need to 'transpose' a Bible quotation word for word, and exactly into the metaphor used by Lindir. (I doubt that Tolkien would ever be so crude and clumsy.) You seem to think that because no Bible reference exactly corresponds one to one to Lindir's metaphor, this indicates that it is unlikely to be a Biblical reference. Not so! The fact that Lindir's metaphor hits a Biblical register, a Biblical note, just makes it more certain that we should stop and ask all the questions we could easily ask ourselves about Lindir's metaphor if it were not Biblical at all.
We disagree on the basic principle and terminology: a Biblical reference isn't what you assume it to be. A Biblical reference isn't "hitting a Biblical register, a Biblical note". A Biblical reference is precisely what you discount as "crude and clumsy". There were many authors who did this - and did it well to boot. For the simplest example by Tolkien himself think about Ainulindalë which is "a transposition" of a part of the Bible - mostly the beginning of John but also of Genesis.
However this isn't my main point. I would agree with your seeing in what Lindir says a reference to Psalm 123 if there was any mention of the shephed caring for the sheep in what Lindir says. I would agree with your seeing any Biblical reference (in the exact sense of the term) if there was any Biblical fragment (it's not so much about words - which you seem to assume with "word for word" - but about topics, ideas) which emphasizes the fact that a shepherd can distinguish among his sheep. Neither of those is true.