Whether there is, or isn't a "reality" to our world, and how we can discover what is real, if there is one, is pretty much central to the philosophic enterprise.
And sceptics, such as Socrates, taught us to question the level of understanding we have of even our must fundamental ideas and definitions, which brings our ability to even define or characterize what "reality" is, into question, which puts the burden of justification on any claims made by advocates of scientific realism.
That rationalism is an unreliable tool to discover any possible reality, has become increasingly apparent, as Kant's Critique of Pure Reason has gotten even more reinforcement in the centuries since. See for example the demonstration that Euclidian Geometry cannot simply be assumed to be true and necessary, and Godel's demonstration that logic systems cannot be reliably used to verify themselves, and the Munchausen Trilemma showing that all justifications of our knowledge are themselves unjustifiable in principle, and the discovery that there are an infinity of different of logics.
This leaves empiricism, and its refinement, science, as the remaining favored potential option to discover "reality" if there is one. And this debate over scientific realism is therefore the byproduct of the increasingly apparent failure of realist rationalism.
This debate has two major aspects to it. One is motivational. Many of the advocates of scientific realism have been advocating for a very limited ontology/metaphysics, that presumes that things like values, and agency, are not included. The objection to such a limited/valueless worldview is behind much of the objection to scientific realism. The other part of the debate is the extension of skeptics to science, not just to rationalism. This skepticism can be applied even without the motivations of questioning a valueless worldview, but many of the anti-realists lean toward skepticism about scientific realism BECAUSE of its valueless inclinations.
Note, elaborating on the skepticism argument, IF science cannot even be defined, as the 20th century debates over the boundary question for science suggests (Verification Principle was refuted, THEN Refutability was refuted, THEN the assumptions behind science, of continually improving verisimilitude, was shown to be logically invalid, and THEN the definition of progressive and regressive Research Programmes was also shown to be logically invalid, etc., etc.) then skeptics often ask, 'how then can science be a plausible candidate for a method to arrive at "reality"'?
Note that not all scientific realists reject values, selfhood, and agency from their ontological worldview. Karl Popper is a premier example of a scientific realist who embraced a more complex ontology that leaves explicit room for agency, and values. Examples of value-based scientific realists show that the dichotomy of values vs realism, that motivates much of this debate, is not itself a necessary dichotomy.