Socionics is not a well-known phenomenon among the general public like MBTI is (often it is literally handed out by major employers and is even used as a hiring tool, at least here where I live in the USA), so gathering precise data about it is really hard, but I think we can make good assumptions about it, based on observations of people we see in our lives.

I can assume that ethics tends to be much more common in women than men. Logic seems to be more common in men than women, but I have noticed many ethical men. In my experience, ethical men are surprisingly more common and appraised among men (and women) than logical female types. Logical female types tend to be far more alienated from both males and females than ethical men are. Intuition seems to be a mostly useless tactic to survival, but is incredibly vital for a small amount of people to have, due to the fact that our intuition is what distinguishes us from other species, like the ability to create technology and vast interconnected road systems and massive cities, unlike literally any other species ever (but cannot be given to everyone, as sensing types need to practically maintain reality and realistically implement/maintain the intuitive concepts that are coming up, like cars or smartphones or computers for example), so I would say that sensing is far more common than intuition among the general population, and I have noticed this as well, out in public with people I interact with.

From what I can see, growing up, an overwhelming amount of females I have met or seen in my life are SF types. Most guys are ST types, but I have seen a decent amount of SF males running around. I haven't really met with many NF types in real life, I think I can literally count the amount of NFs I have met in person on my fingers; I'm surprised at the lack of NFs I have met. I have met a good amount of fellow NTs in real life, we were good friend, and there were a surprising amount of them, much more than NFs. With regards to rationality vs irrationality, I think that there is a perfect healthy balance between rationals and irrationals in the population, at least from what I've seen. I don't think one is more dominant than the other at all.

My idea
Male: ST > SF > NT > NF
Female: SF > NF = ST > NT

As for the quadras, this is what I'm curious about. What do you think the quadra distribution among the general population would be? I feel that it's pretty equal, with a good balance of Alpha/Gamma SF men and women, and a good balance of Beta/Delta ST men, but I'd still be curious to hear what you've seen in your real life with regards to quadras and temperaments among males and females in the general population!