One of the real world beliefs about the Fair Folk is that they are repelled or even damaged by iron. For purposes of this question, let's focus more on the latter: namely, how would an elf manage to live to a triple-digit age without dying of iron poisoning, scurvy, beriberi, kwashiorkor, or, for that matter, anemia?
Just because any element, or compound, might be poisonous, or otherwise dangerous in significant quantity (a significant quantity might be quite small), it does not follow that a lesser quantity might be equally dangerous, or even non-desirable.
It is quite likely that elves or faerie folk already have iron in their bodies, but in healthy and non-threatening quantities.
They also may not be susceptible to scurvy, beriberi, kwashiorkor or anaemia - why should they have that similarity to humans (who are not damaged by dietary iron, although maybe harmed by a non-dietary blade)?
Faeries are only sensitive to metallic iron: Fe0 That is the stuff horseshoes are made of.
Metallic iron is rare on the surface of the earth because it oxidizes. That is why one must smelt iron ore before making metal objects. We do not have Fe0 metallic iron in our bodies or blood. This is why MRI machines cannot tear the blood out of you.
Iron participating in biology is Fe2+ or Fe3+. Those iron molecules occur with companion molecules; for example FeSO4 or iron sulfate, commonly used as a mineral supplement pill. Or an iron ion can be chelated in a molecule like hemoglobin or ferritin. One cannot make a horseshoe out of iron sulfate nor is it magnetic.
Ironically, iron intake for an elf would be the same as for humans.
There's a (human) condition called haemochromatosis, where there's an excess of iron in the blood. Treatments include:
1. low-iron diets;
2. phlebotomy (medical bloodletting);
3. in rare cases (where phlebotomy isn't an option), chelation therapy, a medication that reduces the amount of iron in your blood.
(See the NHS page on haemochromatosis for more details.)
If you assumed that normal human iron levels equated to haemochromatosis in elves, they could undergo similar treatments if necessary. They may simply just not need as much iron, due to a different constitution.
Another option would be for your elves to not have an iron-based blood system. Some arachnids, molluscs, and arthropods have copper-based blood (haemocyanin), which is clear internally but turns blue in contact with air. I'm not sure what the consequences would be of a humanoid creature having copper blood, but it could mitigate the problems with iron. (Wikipedia has some more info here: https://en.wikipedia.org/wiki/Hemocyanin)
The Fair Folk are repelled or harmed by the metal iron, but not the metallic element in general.
The same element can have very different properties when bound to others in molecules, or even when bound to the same element, depending on the molecular structure. The best-known example of this is probably graphite vs. diamond, which are both composed entirely of carbon. Similarly, while the pure elements sodium and chlorine are both toxic to humans, sodium chloride (table salt) is not. So, the danger of iron depends on how it forms molecules, and dietary iron is typically not elemental iron, which means there should be no danger.
How do the fey deal with hemoglobin in their blood?
Whatever your answer to that question is, and I'd strongly suggest handwaving it, will be your answer to how the fey deal with dietary iron.
Traditionally it has been the symbolic magical properties of items that have been important, not their chemical ones. Meat isn't metal, neither are leafy vegetables, so for the purposes of symbolic magic the chemical iron won't matter.
They might use chelation. This is a process in which a compound (often a protein with sulfur moieties or other organic molecule) is ingested (or given through IV in alternative medicine) to bind the metal. Chelation therapy is used for mercury poisoning, and improperly done can be fatal.
I suspect your elves have learned to eat the right plants to chelate iron. In some countries parsley and cilantro are used to reduce mercury load.
The tradition of iron being harmful to faery folk includes a qualifier that people often neglect: cold iron. It is reasonable to suppose that this refers to metallic iron, and that ions (Fe2+, Fe3+) do not count, as @Willk has postulated.
Edit: to make this answer more obvious, dietary iron compounds would then be safe to eat, as they do not contain iron in metallic state.
What those guys got is a contact allergy to iron. The solution is very easy:
In a fantasy setting, and in the absence of a "heal allergy" spell, you can use stinging nettle leaves. The trick is that you have to freezy-dry then - so instead of causing an itch, they will work like natural antihistamines.