You are always allowed to initialize a final variable. The compiler makes sure that you can do it only once.
Note that calling methods on an object stored in a final variable has nothing to do with the semantics of final. In other words: final is only about the reference itself, and not about the contents of the referenced object.
Java has no concept of object immutability; this is achieved by carefully designing the object, and is a far-from-trivial endeavor.