I suspect that some of the RedPill ideas have a grain of truth but aren't necessarily the ideals or standards that we want to codify and hold society to.
Here's an analogy, however shaky it might be: We might have this innate urge to kill someone that really pisses us off or fucks us over in some major way, but society has agreed that killing is a no-no. But no matter how many times you print the laws in gold lettering or carve them in stone, our inner primate sometimes wishes we didn't have these rules so we could just do whatever the fuck we want. Is society wrong?
What makes me think society is not wrong is that in the past we've done plenty of killing and we have little to show for it being unequivocally better than some hypothetical alternative that doesn't exist. E.g. where we are still universally stoning people for wearing the wrong fabrics at the same time or working on the wrong day, and it being clearly the right decision or the determining factor to a successful society. Clearly that's not the case and we've moved on, but because it's so ephemeral of an idea you could imagine an alternative world where even stoning might be ideal, given a vastly different set of circumstances...
Or the death penalty argument, since it's similar - all it takes is one counterexample of innocence to at least give you pause about whether it's a good idea. Even if you maximized the effect of the deterrent (assume you're playing god and you adjust a knob) you're still going to have counterexamples of people being denied justice/fairness. So in the other direction, for the sake of a primitive, heavy-handed deterrent force, you make the abstract higher-order decision to opt for the occasional innocent death, rather than the utmost fairness because you feel there's more value in the deterrent's effects than in the fairness.
Similarly, where I get skeptical of RP is the idea that men have been "in control" forever and yet here we are. If it were such a tried & true methodology or mindset or standard of behavior, why isn't it how we do things 100%? Why don't women see the light in it? Why did the 50s fail to capture people's attention so hard? Why were the 60s and 70s liberation movements so successful if the ideal of the 50s was so rock solid? How could feminism ever have taken hold in the first place?
Some might say: Well then, all this BP stuff, society's rules, etc. is relative. Yes, it's relative because it's abstract and complex and somewhat removed from our most innate, limbic-system responses to stimuli. Some of it is subjective, and some of it depends on circumstances that are inextricably linked. Some things about society we wish we could change but we can't because certain other things are the way they are right now. Maybe in twenty years it'll be a different story. Look at marijuana sales - unthinkable 20 years ago and here we are with legal in several states. Were the naysayers wrong? Were they right? If they were right, then how did it change? If they were right, how right? Is it clearly black & white? No? WELL, BY GEORGE!!
We recognize that those primitive biological responses are there, but that our abstract thinking and efforts in it are sort of pure and "heavenly" and inspiring, if you will. The space race comes to mind - even though it had very primal underpinnings (competition between US and Russia for example; cock-waving), we attach lofty ideals to it and assume that without progress we are stagnant, boring, unchanging, not going anywhere, not taking risks, not advancing the species and fulfilling our need for answers and our sense of completing the puzzle... It's not one or the other.
When people say morals are relative and you can't deny our impulses and all that, I immediately think of the higher-order brain functions that make all this relativistic, subjective, idea-based stuff possible and what it means to be a "complete human". I think that the sign of a truly mature, highly functioning adult (male or female), is to lived a principled life, be proactive, finish what you start, know when to change directions, cooperate with others in mutually beneficial ways, be part of groups and help the group achieve more together (don't be a stick in the mud; give, even if you aren't a natural "leader"), learn and grow as a person, take care of your mental and physical needs and eat properly.
Despite male and female biological differences, a lot of these fundamental principles we have in common. They are higher-order, abstract functions. So we unite in an abstract space that many of us would agree is more interesting, albeit not completely, than the more primitive needs. Those are important too. But I think RP fails to recognize, out of its own quest for self-importance, that these higher order functions are either not done at all, not done correctly, not done at the same level as a man, and counterexamples be damned. We have ARM processors in our phones because of a woman who was smart enough to design the chip and instruction set. If it was such a good idea and changed the industry so much, why wasn't it a man? Again, these higher-order things are accessible to women and many feminists (the wiser ones who don't reject the significance of both male and female biological differences) simply want the opportunity to be allowed to participate fairly in a system that they are indeed equipped for.
My impression of RP is that it's a gut feeling. It's more or less a pseudoscience and a feeling masquerading as good rational thought. Where I think RP fails is in assuming that the biological somehow supercedes the abstract, e.g. just because we have a boner and want to fuck, and just because women sometimes make us feel like less than what we grew up thinking we were supposed to be, we now have an agenda that places our biological needs above even the woman's higher-order brain functioning, principles, and potential. We reduce the heights of a woman to less than our primitive selves, which I think is pathetic and the sign of a weak immature man.
My impression of BP is that it's perhaps higher-order thought without always recognizing the primal needs and the biological impulses and the sheer magnitude of cultural and maybe even genetic/epigenetic conditioning - as if we can just put those things aside and all act purely rational.
That's where I stand - we can have certain elements of fairness and equality of opportunity in our pursuits, largely because if we don't we are denying utmost fairness to even the most occasional/seldom/rare counterexample of a person (which is only the lower bound on reality), while still recognizing the existence of our biological urges and differences. In other words, I think we are foolish to let either of them dominate completely. I think people in both communities completely blow their own ideas way out of proportion, perhaps because it's the internet and it's easy to over-argue a position and write walls of text that don't actually solve anything.