There is a "war" between science / scientism and subjectivism (of sorts), though Nathan greatly misses the mark on identifying who's at war with who.
Science and scientism
When science conflicts with something, it means we have well-demonstrated evidence that that thing is false.
Scientism is the position that science is the only or best way of knowing things (with e.g. maths incorporated into this in one way or other, and maybe one would extend or generalise it to reliabilism for metaphysics). When scientism conflicts with something, it means that thing is based on unreliable ways* of knowing things outside of science.
* People who use such ways may disagree about them being unreliable, but reliability is something that's based on demonstration and measured through accurate predictions, which those ways haven't produced. Never mind that measuring such predictions are done through the scientific method. You can come up with your hypotheses however you want, but in robustly testing them, you'd be doing the scientific method.
"The" culture war
In terms of the (US) "culture war"* between the left- and right-wing (i.e. positions commonly advocated for by people identifying with the respective sides), one finds science much more supporting left-wing positions such as:
- Accepting the science of sex and gender (that LGBT people exist, that such identities are natural and that accepting them is best for their well-being).
- Accepting the science of climate change.
- Accepting the science of COVID-19 (that it's a real thing, 'cause that's the low, low bar much of society is at, and accepting that masks and social distancing are/were effective).
By contrast, the right-wing makes claims about these things based in religion and pseudoscience, e.g. that sex or gender are one and the same and/or strict binaries, that God made two genders, that climate change isn't real despite the overwhelming evidence and overwhelming support from scientists studying this, that God looks after the Earth or Jesus will come back any day now, so we don't need to worry about the climate.
There has been an increasing distrust of science / the scientific community among the right-wing, driven in large part by right-wing talking heads turning the things above into political issues: it's not just some facts of reality, but it's instead the libs trying to destroy your way of life. The right-wing's distrust of science is likely also supercharged by RFK Jr., the Trump-nominated secretary of health, being anti-vaxx, spreading COVID misinformation, HIV/AIDS denialism, chemtrail conspiracy theories, etc. Historically, these conspiracy theories weren't specifically tied to a political leaning.
Though the left-right conflict isn't specifically about scientism versus subjectivism. It tends to be more about cooperation versus competition (whether we're talking about social or economic policies). Left-wing ideology wants to raise up those trampled by society, so we succeed together. Right-wing ideology is more about individual success and "us versus them": you succeed by trampling over others to reach the top, and you need to proactively trample on minorities to prevent them from trampling on you. How the right ended up on the side denying science on every issue where it applies may be an interesting question, but it's beyond the scope of this answer.
* The use of the term "culture war" arguably minimises the fact that many of these issues are about basic human rights and human well-being. But for the right-wing (at least as their talking heads tries to whitewash it), it's merely about protecting their culture where life is a utopia if you don't give people these rights nor shown any concern for these aspects of human well-being. Hence the "culture war" label.
What "subjectivism" is science in conflict with?
Subjectivism is the belief that reality is subjective. There are people who speak about "my truth and your truth", but this is a fairly fringe layperson view. And even for those people, it doesn't seem like a strongly-hold and well-thought-out position. It's more just a thought-stopping or debate-stopping technique.
Science / scientism more commonly conflicts with things that are based in subjective experiences (though not quite subjectivism):
Religion often makes claims contradicted by science (e.g. claims about the history of Earth). Religion is fundamentally based on ways of knowing things outside of science (whether that be "faith", questionable spiritual experiences or wishful thinking), so conflicts with scientism.
One can say the same about "supernatural" or "non-physical" claims in general.
Pseudoscience often makes claims contradicted by science (e.g. claims about whether some medicine or device or technique works). Pseudoscience is fundamentally based on things outside of science, like unreliable anecdotes, cherry picking or otherwise questionable inferences.
Authoritarianism often makes claims contradicted by science, and its way of knowing things is just trusting and believing what supreme leader says. Well, to be more accurate, it's based on a range of cognitive biases - authoritarians often e.g. try to stoke fear and hatred of minorities, and then present themselves as the solution to the non-existent problem created by said minorities.
Though authoritarianism conflicts with anything that opposes its authority: science, robust statistics, independent journalism, free speech, comprehensive unbiased education, independent courts, independent religion, etc. Though they tend to be content with journalists, courts, religion, etc. that they've taken over or as long as those support them.
There are also people who feel that the diagnostic and reductive sense of science invalidates and strips away their identity. This is a reasonable view when one has seen too many people abusing science or appeals to science with a disregard for empathy and human well-being. But it's more generally the case that science and the scientific community supports those identities (at least if we're talking about gender).
Nathan severely misses the mark on identifying said conflict
He presents scientism as insisting that reality fits into strict categories, but this is a reality-denying anti-scientific view. Science overwhelming points to reality not fitting neatly into the categories we make up.
At best, this strict categorisation view is a few centuries out of date. Or it surrenders science to the people (generally laypeople) who e.g. insist that "basic biology" agrees with them, even when their view is contradicted by biology, as attested to by a whole lot of scientific papers and the overwhelming majority of biologists. Or they're making dogmatic unscientific assertions about biology, which is still not science.
Conversely, he says that subjectivism recognises that there aren't strict categories. Yet those who make controversial claims about the existence of such categories generally do so based on religion or cognitive biases that stand opposed to science. One can certainly have a subjective view that such categories don't exist, but it seems inaccurate to say this is the view "at war" with science.
The part of the video about gender is very confused.
In addition to incorrectly characterising scientism as boiling things down to strict objective categories:
- He says scientism, through psychology, recognises that there is "considerable crossover" in gender traits, and that some people don't fit into traditional gender roles.
- But then he also says scientism cannot recognise the inner self (which is a collection of such traits).
It seems fairly self-contradictory to say people obviously possess certain traits, but that it would be denying reality to recognise that someone possesses a group of such traits.
He says that scientism cannot recognise the effects that speech has on "the conceptual framework" (how people think). But this, again, is a dubious characterisation of scientism. He's trying to exclude the science of psychology from scientism, which is explicitly defined by encompassing science.
His video thumbnail and description prominently mention Jordan Peterson and Greta Thunberg. Though there is barely 1 mention of either in the video itself, I expect he'd put Peterson on the side of scientism and Thunberg on the side of subjectivism, which would perfectly capture the problem with his entire thesis.
Peterson may have a facade of being uncompromisingly analytical, but his most significant claims are non-scientific and/or contradicted by science. In particular, he is on the side of trying to insist that there exists strict objective gender categories.
Thunberg may be known for making emotion-filled arguments, but her position (that climate change is real, caused by humans and would have, and is having, significant negative effects on humans) is strongly backed by science and the overwhelming majority of the scientific community. She stands with scientists, against those who deny science.
When one accepts the science, and realises how much a few greedy and callous rich people have done (and continue to do) to oppose and suppress it, often knowingly so, her anger seems perfectly understandable. Though that's besides the point.
Having emotions doesn't mean one stands against science, and never showing emotion doesn't mean one has a scientific mind. Though Peterson often expresses anger too, and constantly expresses contempt. But those emotions "don't count" when people on his side criticise people for "being emotional"... which usually isn't even relevant to the merits of what they say. There's a very narrow sense in which emotion stands against science: when one's claims about what's true ultimately boils down to what one prefers (cognitive biases), and that applies much more to Peterson's gender categories, as opposed to Thunberg's claims about climate change.
In short, what Nathan calls "scientism" seems to be internally inconsistent, with little relation to science, and is instead what's being peddled by some pseudo-intellectuals, despite them frequently standing opposed to the scientific community broadly, and their views often being based in anything but science.