Maybe we should wonder about that, when Lindir implies that Elves are neither sheep nor shepherds.
Also, are there any 'shepherds' for Men? The Valar seem to be shepherds for Elves. They have built them a wonderful home in Valinor. They protect them (sometimes) and look after them (to some extent). But, are they being 'shepherds' to Men (or to Hobbits)? Or, did they wash their hands of Men after the downfall of Numenor? "Let's leave them to Eru. We don't understand them at all."
We don't really know enough, if we are first time readers, to ask some of these questions, but Lindir's stance that Elves are neither sheep nor shepherds should lead us to start to wonder, and to wonder if that does not imply something wrong.
I have a lot to say about this whole topic as I am of the opinion that seeing a Biblical reference here is reading something into the text which wasn't intended in it. There's a lot of Biblical references in LOTR but this just isn't one of them.
However this is not what the main topic of my post is about. The thing this discussion is lacking is
context. When and in whose presence does Lindir speak those words? Or - to put it differently - who are the main "guests/strangers" (i.e. not regular inhabitants) in Rivendell in this moment? In one chapter we will learn that a lot of people (Humans, Elves, Dwarves etc) have come but for the moment all that the reader knows is that there were 2 sets of "new strangers" (as opposed to Bilbo who by now is settled in there): Aragorn with 4 Hobbits and Gandalf. And here I come to your question: "But, are they [the Valar] being 'shepherds' to Men (or to Hobbits)?" - even if the answer is "no", there is someone who is a "shepherd" to Men and to Hobbits. It is Gandalf.
Lindir speech makes a lot more sense when viewed like this:
- Bilbo banters with him and says: "They’re as different as peas and apples.’" meaning "Men and Hobbits"
- Lindir says that there might be a difference: "‘Maybe."
- but he doesn't see it because it is not a difference he can perceive because he is not a mortal: "To sheep other sheep no doubt appear different,"
- however he realizes that there is someone who isn't a mortal (so "not a sheep" to use his imagery) but who surely can make the difference and that is because he is tasked with shepherding Men and Hobbits i.e. an Istar: "Or to shepherds."
- and then he explains what is the difference between the general Elf perspective here and Gandalf's: "But Mortals have not been our study." - this clearly implies that the shepherd in question here is someone for whom the Mortals were their study. This is clearly one of the Istari, they are the ones who learn about the Mortals in Middle-Earth.
Just take a look at all the other uses of the word "study" (or "studied") in LOTR (I discount only those in which "study" is used to refer to a room at Bag End):
- "But Hobbits have never, in fact, studied magic of any kind"
- "A love of learning (other than genealogical lore) was far from general among them, but there remained still a few in the older families who studied their own books, and even gathered reports of old times and distant lands from Elves, Dwarves, and Men. "
- "The greater families were also concerned with events in the Kingdom at large, and many of their members studied its ancient histories and legends. "
- "He has long studied it, seeking the lost secrets of their making; but when the Rings were debated in the Council, all that he would reveal to us of his ring-lore told against my fears "- Gandalf on Saruman
- "Pippin was standing studying the sky and weather." - this doesn't refer to learning at all, it uses a meaning akin to "surveying, watching with interest"
- "I had to study you first, and make sure of you." [Aragorn in Bree] - this is debatable as it refers to him learning about them but it is mostly about gaining intel on the four Hobbits.
- "But Mortals have not been our study." - the passage in question
- "Have I not earnestly studied this matter?" - Saruman on Saruman
- "But unless you have more skill even than Saruman, who has studied here long, you will find naught that is not well known to me, who am master of the lore of this City. " - Denethor on Saruman
- "But Saruman has long studied the arts of the Enemy himself, and thus we have often been able to forestall him. " - Gandalf on Saruman
- "It is perilous to study too deeply the arts of the Enemy, for good or for ill." - Elrond on Saruman
- "‘Not well,’ said the old man: ‘that would be the study of many lives " - Gandalf on Fangorn
- "With a new sense of responsibility he brought his eyes back to the ground near at hand, studying the next move. " - Sam, once again with a meaning closer to the quote about Pippin
- "He studies the signs: the Sword that robbed him of his treasure re-made; the winds of fortune turning in our favour, and the defeat unlooked-for of his first assault; the fall of his great Captain " - Gandalf on Sauron,
- "I did not spend long study on these matters for naught. " - Saruman
- "It went in at last, and Butterbur’s face was a study in wonder." - a fixed phrase
So discounting the other meanings and a fixed phrase we are left with the word "study" referring to learning about other creatures, mostly in depth and most likely referring to the doings of the Istari (or Sauron in the one example). There also the first two quotes from the Prologue which aren't in direct speech and so use a different register (therefore "studied books", "studied ancient histories" instead of "read books/histories"). However the reference to "studying magic" refers back to the Istari. This can be also reinforced using another of Gandalf's quotes (this time without "studying") which shows a part of his approach to Hobbits:
"Hobbits really are amazing creatures, as I have said before. You can
learn all that there is to know about their ways in a month, and yet after a hundred years they can still surprise you at a pinch. "
What is important here? "Learning" about the ways of the Hobbits. And while "learn" has many more meanings in LOTR and I won't enter here into the exploration of all 178 occurences (in my electronic edition) of them, I want to draw attention to this one: "He is
learned in the lore of the Rings, yet he is not among us " (Galdor on Saruman). The same applies to "knowledge" (47 occurences) - both Gandalf ("Among the Wise I am the only one that goes in for hobbitlore: an obscure branch of
knowledge, but full of surprises. ") and Saruman ("We can bide our time, we can keep our thoughts in our hearts, deploring maybe evils done by the way, but approving the high and ultimate purpose:
Knowledge, Rule, Order; all the things that we have so far striven in vain to accomplish, hindered rather than helped by our weak or idle friends.") make it clear that this an important part of what their whole being as Istari is about.
So I am quite sure that what Lindir meant to say was "There might be a difference between Men and Hobbits. I don't see it because I am not a mortal - mortals would surely see it. Oh, and an Istar whose specialization is 'Mortals' would too.".