Wild shapes are ineligible to use Elven Accuracy
On feats, the PHB says:
You must meet any prerequisite specified in a feat to take that feat. If you ever lose a feat’s prerequisite, you can’t use that feat until you regain the prerequisite.
So our first question is whether we can meet the prerequisites for Elven Accuracy while we are in wild shape. The prerequisite for Elven Accuracy is "Elf or half-elf" (XGtE 74). So how are we to interpret this phrase - your race upon character creation must be elf to later take the elven accuracy feat, or you must currently be in the body of an elf to meet the prerequisite of the feat (as Cezaryx suggests)?
Since Xanathar's does not define what they mean by a prerequisite, how does it describe the racial feats?
A racial feat represents [...] a deepening connection to your race’s culture.
It doesn't seem, on the face of it, that being in wild shape would lessen your connection to your culture, since the druid retains their Intelligence, Wisdom, alignment, and personality. So if all we need to use Elven Accuracy is is an authentic understanding of Elven culture, perhaps the feat can be used in wild form.
What are the limitations of wild shape? As correctly cited by the querent:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.
Feats, including Elven Accuracy, are benefits of a feature 'from another source'. Thus one part of our decision is whether the wild shape is physically capable of using the feat. Again, if all we need is an appreciation for elven culture, the wild shape should be physically capable of that.
Turning to the feat itself, just the small part quoted by the querent says:
Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.
There are certainly plenty of wild shapes that will be making attack rolls using their Dexterity. However, this is not the only part of the feat. In particular, just as there is no flavor text in spells, there is no flavor text in feats. Examining the full description of the feat, we find:
The accuracy of elves is legendary, especially that of elf archers and spellcasters. You have uncanny aim with attacks that rely on precision rather than brute force.
This is not a prohibition against melee attacks just because archers and spellcasters are exemplars; of course an elf with Elven Accuracy is going to to be able to use it for melee finesse weapons. However, what we are trying to determine is the appropriateness of the feat for use with the natural attacks of a Beast. Thus we need to consider, are there any Beasts1 for which their attacks physically resemble those of elven warriors and spellcasters? Certainly there are beasts that rely on precision rather than brute force. But do they attack in such a way that resembles legendary elven accuracy? That is, are they physically capable of attacking in such a way that they could benefit from a deeper connection to the attack forms celebrated in elven culture?
Dating back at least to first edition, D&D elves have been associated with swords, bows, and spells. 5e expresses this in Elf Weapon Training, a racial feature of High Elves. Regardless of class, High Elves have:
proficiency with the longsword, shortsword, shortbow, and longbow.
This is how I would understand the feat - elven culture places an emphasis on training in spells and certain weapon forms that favor accuracy over force. And the kinds of attacks available to Beasts just do not match this 'style' of fighting2, either delivering accurate missile fire, or darting in to deliver accurate thrusting and slashing blows with a long, light weapon and then backing out to parry. Using a bipedal (Humanoid: Elf) body, with two limbs for movement and two hands holding weapons. The Beast forms available to a druid simply are not 'physically capable' of the fighting styles for which the Elven Accuracy feat applies. Can you imagine the druid attacking as a wolf and observers remarking, "Wow, that wolf's bites really remind me of the sword attacks of the legendary elven bladesingers."?
So we have two possible ways to understand the 'prerequisite' for using the feat. Either you must use the feat while you are in the body of an elf (and a wild shaped druid is not in such a body), or you must use it to make attacks in such a way that they rely on your deep connection to elven culture, especially like an archer or spellcaster (and while a wild shaped druid could mentally retain this cultural connection, their mode of fighting would not be like that of elven warriors, even if it used Dexterity for their attack roll). Thus, wild shapes are ineligible to use Elven Accuracy.
Obviously this is a rules interpretation, which is what the wild shape phrase 'physically capable' insists we do, interpret. Most of my games are pretty narrativist and I would be very comfortable with this ruling in them. If I was running a character optimization game where backstory was optional and the concept of 'deepening their connection to elven culture' got me blank stares from the players, then sure, I would let them use the feat with any beast form attack that was clearly based on Dexterity.
1Perhaps any druid casting Beast Spells once they had attained the class feature at 18th level.
2I could see making an exception for Dex-based beast attacks that are clearly rapier-like, for example a stirge or scorpion.