I've read that UUIDs are typically not recommended as a primary key due to size and performance issues on large data sets.
However, would it be detrimental at all to use it on a few of the top level organizational tables? E.g. Organization or Branch, where there are only a handful of entries?
I would recommend that you use serial instead of UUIDs. Why are integers preferable to UUIDs?
In many databases, tables are physically ordered using primary keys. In such databases, new inserts on a UUID will almost always go "between" records, which is expensive. However, Postgres does not support clustered indexes so the underlying data is not ordered.
There are downsides to integers:
Other than space usage, I don't think there is much harm in using UUIDs on a static table. I strongly prefer integers, only resorting to UUIDs in situations where an integer would be difficult to calculate.