An essential dimension on eliminative materialism, and, I believe, the element that determines whether eliminative materialism is open to a self-refutation charge, is the claim that folk psychology is a theory. According to EM, propositional attitudes are theoretical entities in a theory to explain observable behavior. If this is conceded, then the advocate of EM will argue that we have to be open to the possibility that these theoretical posits could be replaced by posits that are more scientifically adequate. Those who think eliminative materialism is self-refuting also typically challenge the claim that folk psychology is a theory.
But, to me, it seems very clear that at least some propositional attitudes, like my desiring a steak dinner, are not theoretical posits, but are rather states of affairs of which I can be, and am, directly aware.