Should I take an academic class on rationality?

Subjective perceptions and the relations between humans are also part of reality.

A more charitable phrasing: you view feminism as more concerned with instrumental rationality than with epistemic rationality.

my basic sketch of it is that philosophy and rationality are overconcerned with objective reality, and that we should instead focus on how perceptions are subjective and how we relate to one another.

The subjectivity of our perceptions and how we relate to one another are themselves parts of objective reality.

To steelman the position you're attributing, if philosophy and rationality have been paying too little attention to those parts of objective reality, then they need to focus on those as well as, not instead of, the rest of reality. Or to put that in terms of a concrete example alluded to elsewhere in the thread, nuclear power plants must be designed to be safely operable by real fallible humans.

But they do attend to these things already. Bayesian methods provide objective reasoning about subjective belief. Psychology, not all of which is bunk, deals with (among other things) how we relate to one another. Engineering already deals with human factors.

my basic sketch of it is that philosophy and rationality are overconcerned with objective reality, and that we should instead focus on how perceptions are subjective and how we relate to one another.

I'd go even further than that, and state that the very notion of an objective reality onto which we can project our "rational" action without regard for social or moral/ethical factors is somewhat peculiar. It seems to be very much a product of the overall notion of λόγος - variously given the meaning of "argument", "opinion", "reason", "number", "rationality" and even "God" (as in the general idea of a "God's Eye View") - that seems to permeate Western culture.

Needless to say, such "logocentrism" is nowadays viewed quite critically and even ridiculed by postmodernists and feminists, as well as by others who point out that non-Western philosophies often held quite different point of view, even within supposedly "rational" schools of thought. For instance, the Chinese Confucianists and Mohists advocated a "Rectification [i.e. proper use] of Names" as the proper foundation of all rational inquiry, which many in the Western tradition would find quite hard to understand (with some well-deserved exceptions, of course).

overconcerned with objective reality, and that we should instead focus on how perceptions are subjective and how we relate to one another.

I hope these people are kept far far away from nuclear plants. And regular factories. And machinery. Actually, far away from any sharp objects would be the best...

They are very much the product of a dominator culture as opposed to being more focused on, say, care and nurturing - be it of fellow human beings or our natural environment

For someone with a strong interest in or preference towards caring and nurturing, rationality is still very useful. It helps you learn on how to best care for as many people as possible or to nurture as many pandas (or whatever). Caring and nurturing still have win-states, they're just cooperative instead of competitive.

They are very much the product of a dominator culture as opposed to being more focused on, say, care and nurturing - be it of fellow human beings or our natural environment, a real-life symbiote without which our communities cannot possibly thrive or be sustainable.

"Winning" means maximizing your utility function. If you think that "care and nurturing" are important, and yet you failed to include them in your utility function, the fault lies with you, not rationality. Complaining about rationality not taking into account care and nurturing is like complaining about your car not taking into account red lights.

LessWrong folks like to talk about their pursuit of a "Friendly AI" as a possible escape from this dilemma.

What dilemma?

But it's not clear at all just how 'friendly' an AI could be to, say, indigenous peoples whose way of life and culture does not contemplate Western technology.

An AI friendly to Western values would be a tool through which Western civilization could enforce it values. If you don't like Western values, then your objection is against Western values, not with the tool used to facilitate them.

As a general rule of thumb, our developments in so-called "rationality" have not been kind to such groups.

I don't find that to be clear. The mistreatment of non-Western people can arguably be attributed to anti-rational positions, and my most measures, most people are better off today than the average person was a thousand years ago.