Does Theravada posit the selflessness of phenomena? It is generally taught in Mahayana monastic universities that Theravada does not posit the selflessness of phenomena. There it is taught a dichotomy exists between the tenet systems employed by various Buddhist traditions:


The selflessness of persons
The selflessness of phenomena


In Mahayana texts it is often said that the self of persons and the self of phenomena comprise the "two selves" that are refuted. It is said that Theravada only posits and thus refutes the self of persons.

This is a commentary on a textbook used in Buddhist monastic universities in India/Tibet written by a Geshe Lharampa:


  For the, "Vaibashika school, there are 3 divisions and 18 subschools,
  one of which is the Theravadan school)"
  
  ...
  
  Selflessness of phenomena is not asserted because the Vaibashikas
  assert that an established base is pervaded by self of phenomena i.e.
  even though the V assert selflessness of person, they do not assert
  the selflessness of phenomena.
  
  Within existence, there are two aspects – person and phenomena. When
  one talks about selflessness of person, one is referring to the
  concept of “I”. When one talks about the selflessness of phenomena,
  one is referring to one’s 5 aggregates, all outer objects and
  everything other than concept of “I”. The V school doesn’t assert the
  selflessness of phenomena because they hold the view that phenomena is
  truly existent from its own side.


Emphasis in the original. The point I think is that a dichotomy is made between persons and external objects. The former is said to lack a self, but external objects are considered to be real or truly existent. Some Mahayana tenet systems say the latter also are unreal and not truly existent.

What do self-identified Theravada proponents think of this? Is this how you'd characterize your school or you understanding? Do you identify with the Vaibashika school?
The Vaibashika school doesn’t assert the selflessness of phenomena
  because they hold the view that phenomena is truly existent from its
  own side.


In my opinion, the Theravada view according to the Pali suttas imply that:


The self (of persons) is not truly existent.
Whether non-self phenomena are truly existent from its own side or not, is (probably) not important towards the path to the end of suffering. (See the Parable of the Poisoned Arrow, Parable of the Simsapa Leaves and the Discourse on the Unconjecturables)


Of course, there may be a lot of Theravadins out there who dispute my second statement above, and would assert that all non-self phenomena are truly existent from its own side.

EDIT: Just to make it clearer:

All sankharas (conditioned and/or compounded things) are subject to change, arising and passing. Nibbana is not subject to change, arising and passing. Both sankharas and nibbana are empty of a self. But this does not mean that sankharas and nibbana are not truly existent. The self is definitely an illusion, but the world, transient as it is, may not be an illusion. Whether the world is an illusion or not, is not important to the path to the end of suffering (according to Theravada, in my opinion).