As always, it depends what you’re trying to do…

If you are looking at maintaining relationships between Things, probably the easiest way to look at it is to separate the entities from their relationships (i.e. model it as a digraph with nodes and edges - you could take a look at https://github.com/bitwalker/libgraph for inspiration).

Other than that, looking up other entities by some kind of key is a pretty common approach. How that is implemented depends on what you are trying to achieve (in detail). For example, https://github.com/lau/tzdata provides a timezone database for elixir - it builds the data and relationships in ets on startup (and periodically updates on a schedule when timezone databases update) and provides data back to consumers via lookups on the ets tables. Incidentally, it is building links between entities as part of the database build process to allow alias names for timezones.

What you’re describing sounds a lot like ETS except for the compile-time stuff.

The stdlib uses ETS to store graphs (see :digraph and :digraph_utils) because it’s a mutable key-value store that can be shared with other processes.

For a simpler example, here’s an Advent of Code solution from the 2018 problems that uses an ETS table as a doubly-linked circular list:

Each element in the list has an identifying “value” and the values of its left and right neighbors; the list is traversed by repeatedly looking up entries by the first value and then recursively following the links.

For that problem, the structure was really convenient: each update was a fixed, small number of steps way from the previous update and inserted or removed a single element. That meant changing three entries in ETS, versus rewriting every following entry in a map or list.

(emphasis mine)

I think we might have a case of the xy-problem here: You are looking for help with your supposed solution, but do not give us the full problem which makes it difficult to reason about the solution space. We’re slowly getting closer, as we now know that what you actually want to do has very little to do with ‘compile-time registries’.

You think you want to use bidirectional relationships between e.g. parents and children. However, what would you use these relationships for?
In object- and class-oriented languages where we deal a lot with inheritance, (bi-directional) relationships see a lot of use, especially since pass by (mutable) reference is very common, which is what gave rise to Joe Armstrong’s famous quote You wanted a banana but what you got was a gorilla holding the banana and the entire jungle.

In an immutable functional language such as Elixir, we’d model the problem usually in a very different way where these mutable references are not needed. In these situations we often pick only one direction to go in (such as only parent → child) and that is how we fill in our structs. This is what e.g. Ecto’s relationships use.

But say we are indeed trying to model the ancestry of a family of humans, which is one of the few cases where indeed relationships in both directions might be important. For instance, we want to figure out who all the nieces and nephews of a particular family member are.
In that case, we use a dedicated graph datastructure. (which can be implemented under the hood in a number of ways on an immutable system, which I won’t go in here as it’s not important when using them). One example might be using libgraph but there are other libraries as well.