This question takes some untangling, and the untangling I'm inclined to do will strike some people the wrong way, mostly for the wrong reasons. There's too much politics in science these days. But at any rate...
First: 'Scientism' is a particular thing-in-itself that is only tangentially related to any particular philosophy of science. Scientism is a type of faith built up around the concept of science, one which imagines 'Science' as a thing that can solve all human problems. This concept of 'Science' as a thing isn't anthropomorphized in the way that (say) God is anthropomorphized within certain religious sects: it isn't a conscious actor or entity. But one of the hallmarks of scientism is that science is referred to in much the way one would refer to a magic wand: generalized assertions that anything is possible if we only know the right utterances and gestures to make, but no real interest or regard for the gritty details of theoretical assumptions, methodological standards, research practices, or any of the things that actual scientists must deal with on a daily basis.
Positivism, anti-positivism, and instrumentalism are different understandings or modes within the philosophy of science, none of which is intrinsically given to scientism, and none of which is immune. Loosely speaking, these modes are as follows:
- Positivism holds that we must be 'positive' of our theoretical statements by empirically testing them against the evidence of our senses. Positivists are usually anti-metaphysics and often anti-religious, largely because positivists connect strongly-evidenced theory with metaphysical notions of 'truth', and thus oppose any metaphysical notion that is injected without evidentiary support
- Instrumentalism is much like positivism, except that it rejects the theory-truth connection. A good theory is a theory that works — that lets us do something in the world — and that's all that matters. They tend to be somewhat more ambivalent about metaphysics, mainly because the question of whether a metaphysical theory 'works' is more difficult. Clearly a theory that God exists 'works' for many devoutly religious people, in the mundane sense that it alters their behavior and attitudes, so...
- Anti-positivism notes that most of the things we do as human beings are matters of value and meaning that aren't really subject to empirical evidence. I mean, we can clearly see that diamonds, gold, and Marvel Universe movies have high value to people, but what we cannot see is why they have value, or (put another way) what meanings we attribute to these things that gives them value. One cannot treat a society as one would a physics problem, and thus that calls for a different form of science.
Positivism falls into scientism when people blithely assume that unanalyzed, un-researched, undeveloped, and sometimes completely unknown theory must be true, because it's all 'Science'. A frequent example of this is people who assert that all subjective experience is reducible to objective material properties because, you know... everything is physics. It doesn't matter that neuroscience isn't even close to establishing that as an empirical fact; they assert that physics is the underlying fact of all phenomena (an article of faith), and therefore all mental phenomena must be reducible to physics.
Instrumentalism falls into scientism in the typical pseudoscience way: a blind assertion that correlation and causation are the same. People hear stories that others took hydroxychloroquine and their Covid-19 infection went away; they convince themselves that HCQ works for that particular function; they embrace the theory as functional. It's 'Science' in the loosest, most stupid sense, but it's still 'Science' and thus can't be wrong.
Anti-positivism turns into scientism when it tries to extend itself outside of the realm of human value-action. We see this with religious movements like creationism, and certain secular social movements: ethnocentrism, eugenics, anti-feminism, climate change denialism, etc. Here one tries to use (often oddly constructed) scientific assertions to promote or counter sociological values. It's one thing to have conflict over the roles of different individuals within society. Pragmatically speaking, some people are valued more, some less, and this will be an eternal bone of contention until we finally manage to achieve something like the Star Trek society (or Huxley's "Brave New World"). However, it's quite another thing to say that 'Science' proves that some people are more valuable than others. Empirical science isn't suited to produce value judgements of that sort.