If empirical undecidability is indeed a disease then philosophy is afflicted by it in almost its entirety, materialism included. The basic tenet of materialism, that everything is matter, is as undecidable empirically as the basic tenet of theism, that God exists (especially since the meanings of "matter" and "God" have been stretched to a point of vacuity). Attempts to eliminate undecidable (a.k.a. metaphysical) commitments altogether, undertaken by early Wittgenstein and logical positivists like Carnap, eventually revealed themselves as based on... metaphysical commitments, see van Fraassen's Against Naturalized Epistemology. "Language is far more complex than logicians and the author of the Tractatus imagined", wrote the author of the Tractatus some years after suggesting that the only meaningful sentences were those of empirical science. Nothing short of radical skepticism, which refuses to assert or deny anything at all, escapes non-empirical metaphysics, not even "pure" sense empiricism detached from materialism, a la Quine. Indeed, one needs to accept some non-empirical methodological principles to even stage and make sense of empirical observations and experiments, see Friedman on relativized a priori.
"Nothing is in the intellect that was not prior in the senses". This motto of sense empiricism is itself non-empirical. And Aristotle, to whom it is attributed, was an objective idealist (his ontology included universals, souls and even the divine intellect), and the one who coined the term "metaphysics". Aristotle also believed, like Peirce, Husserl, or Gödel more recently, that we directly perceive some categorial aspects of objects in addition to purely sensory ones, that extends the scope of "empirical" without introducing anything supernatural.
As far as metaphysical commitments go, existentialism is leaner than Aristotlelian essentialism, theism or materialism. It is somewhat an exaggeration to say, but not by much, that an existentialist greets the traditional idealism/materialism and realism/phenomenalism divides with a big "who cares". They are dismissed as intellectual games that obscure the (non-intellectual) "truth" of existence. Heidegger, arguably the most prominent existentialist rejected the Sartre's motto "existence precedes essence" in his Letter on Humanism for... being metaphysical: "But, the reversal of a metaphysical statement remains a metaphysical statement. With it he stays with metaphysics in oblivion of the truth of Being". Quite an unlikely alignment with the early Wittgenstein and Carnap.
As a philosophy of human action, ethics, existentialism is largely indifferent to (traditionally understood) epistemology and ontology. At best, they are secondary wheels, which may or may not help with the "truth of Being". But if an existentialist wants them anyway there is a wide variety of options to choose from, including materialist ones. The supposed incompatibility with materialism is based on taking the latter as the crude mechanistic materialism a la Hobbes and du Bois Reymond. The problem is that its (very much metaphysical) determinism rules out human freedom, the cornerstone of existentialism. But even Marx's dialectical materialism already relaxes determinism, especially in its Lukác's version, which Sartre himself came to favor in 1960s. Other versions of non-reductive materialism can easily accomodate existentialists with materialist leanings too, e.g. Davidson's anomalous monism, or Kane's libertarian materialism, or better yet Nancy Cartwright's "dappled world", emerging out of proto-material deep flux. Timpson argues in Quantum Bayesianism that statistical interpretations of quantum mechanics fit perfectly with her
"...ontological picture for science in which objects primarily have dispositions or powers and it is only when these powers interact in highly contrived, or highly specialised, situations that they will give rise to the repeatable, regular behaviour that can be described by the kinds of general statements we traditionally think of as laws of nature, or as lawlike truths... the world just is arranged in such a way that we do get consistency between the behaviour in these different domains, some governed by some laws, others by others, some not at all."
And this in turn fits perfectly with a third person perspective on an existentialist worldview.