It isn't universal, though like you point out it seems it must be.
For example, we can say that given two objects, all of whose properties are the same, we can say that they are similar and not the same. In Leibnizs language they are indiscernible.
This point of view is used in modern algebra, where the technical notion is called isomorphism.
And it's taken as a basic principle in Category Theory, where one 'ought' not to say that two objects are the same, but isomorphic.
This might be seen as a hair-splitting distinction; and it is, but it turns out to be a useful one.