The logic from the article on that point is a reductio ad absurdum on the eliminativist's implicit distinction between reality and illusion. That distinction presupposes the intuitive, "folk" concept of the mind.
A strict eliminativist can talk only of causal relations that lead to different effects or natural patterns. "Illusion" is a pejorative term that assumes there are mental representations that can be right or wrong, adequate or inadequate.
I don't say reality is an illusion. On the contrary, I say illusions are real as effects of causes. Illusions may not be what we think they are, but precisely that error in thinking is inconsistent with the eliminativism I reject.
If you were unclear with any of this from the article, you could have just asked for clarification instead of snootily dismissing the lot of it.
I read your article on science and beliefs. First of all, I’m not a scientist. My background is in philosophy, albeit in the science-centered, analytic or naturalistic tradition. I’ve written numerous criticisms of scientific institutions, new atheists, and philosophical naturalism (some links below). Still, I accept naturalism as the best starting point in late-modern philosophy, because science does command respect.
I agree that investigations start from assumptions. Scientists have institutional assumptions, summed up as methodological naturalism and as also what the Frankfurt School called instrumental rationality (industry-friendly pragmatism or progressive Luciferianism). More narrowly, scientists have various personal prejudices, but the strength of science as a method is just that those biases get filtered out by the independent testing of the hypotheses. Science begins but doesn’t end with presumptions, since scientists follow the evidence rather than resting on dogmas. These may be simplifications, as Thomas Kuhn would point out, but they show how science differs from pseudoscience and from religion.
You say, “science is no more ‘objective’ than astrology—it simply makes different assumptions.” That’s preposterous. Astrology is unfalsifiable and is therefore pseudoscientific in Popper’s sense. Scientific cosmology is empirical, falsifiable, and tentative. Astronomers gathered evidence to tell us what the stars really are. By contrast, astrologists use anthropocentric metaphors to flatter, comfort, and con people. Astrology is a kind of self-help therapy, not a science or a theory that explains the natural facts.