The insincerity objection is often raised against skeptical positions (nominalism, anti-realism, anti-intellectualism, solipsism, etc.). An ancient anecdote tells of a skeptic, who taught that actions make no difference, jumping away from a cart that was about to run him over. When asked why he jumped if it makes no difference he responded "Ah, it is because it makes no difference that I jumped". The objection is that where the mouth is the money is not, professed dibelief in universals, reality, meaning, other minds, etc., is accompanied by behavior that indicates otherwise.
NE declares that everything is subject to revision, including NE itself, in the face of recalcitrant experience. If that is the case then it should whole-heartedly embrace say Husserlian phenomenology or mystical insight if those prove to be practically successful. And in some areas they might, e.g. heuristic metaphysics, or ethics, or aesthetics. What "practically successful" means is open to interpretation, but according to Quine himself even in science choice between theories is based on pragmatic considerations due to underdetermination by (empirical) evidence. Such considerations may be interpreted as benefiting from some non-empirical experience, e.g. Husserlian "ideal perception". But Quine certainly favored science and scientific method, as I suspect do most philosophers who self-identify as naturalists, and mostly did not venture into areas where alternatives might come into play.
It may not matter in practice if one stays within a recognized provenance of science, but is NE, as practiced, vulnerable to the insincerity objection? Was it actually raised, are there good responses? Is the objection effective at all? According to Wittgenstein the task of philosophy "is not to explain anything, but to leave everything as it is", so how one behaves might be purely pragmatic, indicating no philosophy.