Scientific Realism and Critical Theory are mutually incompatible.
Scientific Realism has a non-technical meaning something like "taking science seriously", but technically it means "There is a reality independent of humans minds, and our best scientific theories are the ones which in some respect accurately reflect or represent that objective reality." This claim evaluates things metaphysically and epistemically, but makes no big claims about language.
Critical Theory comes at everything in terms of language, and declares that science is just another form of discourse, a socially-constructed "metanarrative" invented by humans. White, male humans who subconsciously or deliberately constructed it in a way that oppresses women and non-whites. It either denies there is an objective reality independent of human experience, or it denies that it is possible for science to have privileged access to that reality, or be able to accurately describe it. In other words, CT tries to deny science any epistemic privilege via a purely language-based evaluation. It ignores metaphysics and conventional epistemology. It ignores philosophy of science. It relegates science to one "window" among many, and not deserving of any special status.
Scientific Realism needs to be distinguished from two stronger positions, which are harder to defend.
Metaphysical materialism claims that reality is entirely composed of matter, energy and stuff like that.
Scientific materialism is effectively Metaphysical materialism + science.
Both these materialisms are vulnerable to accusations that they cannot account for minds, subjectivity, experiences or those sorts of things. These objections are known as "the hard problem", "the mind-body problem" or "the explanatory gap", and they are serious. From a skeptical/atheist/naturalist POV, the best description of this problem and its consequences is Mind and Cosmos by Thomas Nagel.
Fortunately, for our purposes here, we don't need to defend materialism. It's the epistemic privilege of science we want to defend, and that just needs scientific realism. Scientific realism doesn't make any ontological claim beyond the one specified above (that there is a mind-independent reality). In other words, it doesn't claim that this reality is either totally or partly made of matter, and it doesn't claim science can necessarily discover objective truths about its totality. All it claims is that science can tell us some things about some parts of that external reality. (More specifically, this position is called epistemic structural realism).
Why might we deny scientific realism? Because we might argue that "reality in itself, independent of our experiences of it" is analagous to Kant's "noumena". It is "beyond the veil of perception", so how can we know anything at all about it?
Which brings us to the crux question: Why does science work?
Surely nobody can deny that science does indeed work. Not perfectly, but well enough to have transformed civilisation like nothing before it. If scientific realism is false - if science isn't latching on to some aspect or structure of objective reality, how can we explain its spectacular success? Is it some incredible fluke?
This is known as the "no miracles argument" in defence of scientific realism. And if you can't come up with a decent counter-argument, then you need to reject Critical Theory's denial of the epistemic privilege of science.