Short Answer
The misuse of the scientific methods for epistemological purposes by pseudoscientists or even scientists in domains of discourse that are decidedly broader than scientific knowledge, such as the humanities or political science, is indeed rampant. There are often appeals in arguments that invoke false precision and even scientists, such as those of the logical positivist movement, have been caught pushing science into domains where it has no legitimacy. Stephen Jay Gould was famous for his NOMA.
However, there are no specific "best arguments" to rebut scientism, but rather to rebut scientism requires rebutting the excesses of science. Thus, the arguments that are adduced with science as an epistemological tool improperly used must be attacked as bad science. If one is looking for thinkers who understand and criticize scientism, then one would be interested in those who attack the limits of the scientific methods such as those offered by Popper, Quine, Putnam, Kuhn, and others.
Given the vagaries of the terms 'science' and 'scientism', therefore, one must make arguments on a case-by-case basis.
Long Answer
"...sometimes philosophy should clarify and distinguish notions previously vague and confused, and clearly this is meant to fix our future meaning only. But this is clear, that the definitions are to give at least our future meaning, and not merely to give any pretty way of obtaining a certain structure."
Frank P. Ramsey
From MW's entry 'scientism':
Definition of scientism
1 : methods and attitudes typical of or attributed to the natural scientist
2 : an exaggerated trust in the efficacy of the methods of natural science applied to all areas of investigation (as in philosophy, the social sciences, and the humanities)
What Is and Is Not Scientism
Much like the term 'science' has a plethora of meanings, so to does 'scientism'. One of the recurring themes in philosophical discussions is what exactly constitutes something everyone takes to exist, but none seems agreed to. In the case of science, this is the infamous demarcation problem, among philosophers of science, anyway. The WP article on scientism exhibits some of the same issues with various characterizations and factions maintaining views. The article you cite also attempts to grapple with 'scientism' by defining four combinatorial flavors over two dimensions, a strong-weak axis and a broad-narrow axis. What everyone should agree upon is that there is no universal consensus on what constitutes 'scientism' in the same manner as the term 'science'.
Stanford Encyclopedia of Philosophy
One quick measure of the term is to scan the entries in the SEP. A quick read of a search for scientism in the SEP at the moment indicates there are 35 entries that the term occurs in despite it having no entry of its own. Those entries include references to Hayek, Wittgenstein, the Vienna Circle, Wundt, and Neurath among others. with such variations and tangential usage to so many, it's tough to give a simple response. The article you cited attempts to address some of the poorly conceived attacks on scientism, whatever that may be, so let's do a quick review of the article.
How Not to Criticize Scientism
The article you have cited tends to tackle the most general specious equivalence that occurs; enemies of science, or at least a fanatical belief that it is a bad practice tend to use it as a pejorative and then conduct strawman attacks, whereas proponents of science often see nothing wrong with the primacy of the various scientific methods as an epistemological virtue and attempt to defend science by showing how loaded language and other fallacies misrepresent the scientific enterprise.
This paper argues that the main global critiques of scientism lose their punch because they rely on an uncharitable definition of their target. It focuses on epistemological scientism and divides it into four categories in terms of how strong (science is the only source of knowledge) or weak (science is the best source of knowledge) and how narrow (only natural sciences) or broad (all sciences or at least not only the natural sciences) they are. Two central arguments against scientism, the (false) dilemma and self-referential incoherence, are analysed. Of the four types of epistemological scientism, three can deal with these counterarguments by utilizing two methodological principles: epistemic evaluability of reliability and epistemic opportunism.
It is evidently the intention of the authors to thwart the pejorative use of the term, and provide a taxonomy for further discussion about this matter. They attempt to equate the pejorative use with a more neutral terminology:
It is good to note that when the opponents of scientism are defining scientism, they usually have in mind something closer to scientific imperialism.
Ultimately, however, they do not attempt to settle the question on the value of scientism itself. In fact, they explicitly redefine that controversy:
An advocate of scientism, for her part, needs to show that scientific practice in fact upholds these principles. The debate regarding scientism thus transforms into a debate on the methodology of science.
Logical Positivism and the Methodology of Sciences
It is no unreasonable claim to say that the most radical defenders of scientism were the logical postivists. Their research goals self-articulated the effort to eliminate metaphysics and reduce philosophy to a branch of the sciences. A good primary-source survey of important, developed logical-positivist thought is Logical Positivism by Ayer. Before reading primary sources, it's a good idea to scan other sources such as Logical Positivism (WP), Logical Empiricism (SEP), and Analytic Philosophy (IEP). Such introductions will give you a good sense of what science taken to philosophical extremes might constitute. Then and only then can you engage in an honest conversation about scientism, as these movements are most strongly associated with the use of science as an epistemological tool.
Those Who Attacked the Excesses of Scientism
What are strong and contemporary arguments for rejecting scientism?
The best way to approach for rejecting science as an epistemological tool may come from the generation of critics who came immediately after the logical positivists, who themselves recognized their own failure to eliminate metaphysics and make science the sole epistemological method. A quick overview personae dramatis can be found in the WP article under the section Critics. Perhaps the most famous among philosophers, W.V.O. Quine wrote an article called the The Two Dogmas of Science which Carl Hempel himself recognized as undermining the notion of objective observation and helping to establish the theory-ladeness of scientific work. Among the general public, Thomas Kuhn "socialized" science by arguing that scientists were very often engaged in political struggles between various paradigms in his The Structure of Scientific Revolution. Popper, Putnam, and Hanson had their arguments too.
Answer
Philosophy is a sophisticated enterprise, and no two philosophers believe the same thing, and in this way worldviews are much like idiolects. The use of the scientific methods as an epistemological tool various greatly from the logical positivists who sought to yoke philosophy as a non-metaphysical pursuit using tools like operationalism, confirmation, and falsification, to those who reject science almost entirely, like religious fundamentalists. As the authors of the article you cite recognize, rebutting scientism generally means rebutting misuses of the scientific method, which range from pseudoscience all the way to the failure of scientists to recognize the value of metaphysical discourse. There are many bodies of knowledge such as the humanities and theology that satisfy various intellectual and emotional needs in people's lives that science simply cannot rival.
Thus, there are no specific best arguments to rebut scientism, but rather depend on the arguments that are adduced with science as an epistemological tool. The strongest criticism of scientism are those which attack the limits of the scientific methods such as those offered by Popper, Quine, Putnam, Kuhn, and others.
