I'm glad that someone is bringing this up because I've been dying to start another thread or maybe continue the one that we had about celebrity couples since there's defintely a pattern with compatibility and type.
Also, from what I've read in Discord about who's dating who, most of them either belong in a supervisor/supervisee, semi-duals, duals or a super-ego relationship.

Hi! Are we talking strictly relational compatibility here, or are we talking about compatibility in efficiency of information transfer between people?
If we're talking relational compatibility, I'll say that if I'm deeply involved with someone, Fi and Se are nearly essential. If we don't have the same depth of understanding about ourselves and our emotions, the way I understand Fi, it's an absolute no-go. Almost the same goes for Se. If we don't speak the same sensual language, or if we don't have fun in a compatible way, there's no way I'm going to stick around. In fact, for most of my relationships, the early processes mostly take place in Se. The big flirting game, meeting each other in that moment of attraction, etc etc. It all depends so much on the subtlety and hypersensitivity of Fi and Se that I really believe a satisfying relationship with anyone not having those qualities would be difficult for me.
If we're talking about transfer of information, there are a few things I could say here too. One is that some people, regardless of type, are more trained in writing than others. I was deeply into writing for a long time, and if I am any good at conveying information well, it is because I learned and care about how to do it. I don't think type has much to do with learning that skill. Ji leads may care about it disproportionately though.
With regards to type, I've had difficulty seeing eye-to-eye with more than a few NeFis, and had difficulty understanding more than a few SeTis. The theory behind CT even gives a possible reason: we metabolize second-to-second information in very different ways, and we are led to draw vastly different conclusions from that same information.
I was into socionics for a long time, but at this point, I have very little belief in it's usefulness. I think it can even promote a harmful idea of relationships. They aren't a business agreement. They shouldn't be thought of as mutually beneficial in the way that socionics promotes duals and the like. Really opposites rarely attract, and you should never ever depend wholly on someone else for perspective, or vice versa. We should just do what feels natural, and have the benefits of the relationship come as a happy surprise later. Going into something with the motive of fitting together like pieces of some metaphysical puzzle is just a recipe for a frustrating and unhealthy relationship / friendship / interaction. Expectations kill genuine human interaction.
Sorry to totally shit on your idea and the rings of benefit! It's something that's rubbed me the wrong way for a really long time and I can get pretty direct about it.

Interesting idea, and also interesting that some people agree and some disagree. My scientific side wants to conduct a controlled experiment, in which I would have a chance to exchange information with 16 strangers, one of each type, and rate how well I was able to understand each person's thoughts, as well as how well I felt they were getting me, and then see what types everyone was. In reality, though, two things--one I don't talk to enough people to have my own idea, and two, I'm unable to be objective. Like for example, my significant other turns out to be my conflictor type in Socionics, and I would naturally like to believe that we have good communication, because I think that's what decent people try to do with their loved ones.
That's why I would do an experiment with strangers, because it would be the closest I could get to being objective.
True, I do tend to find your (@greencoyote) thoughts pretty straightforward and don't have trouble following them. I know one SeTi in real life, and pretty much the same. I don't know if NeTi's on the other hand, have a tendency to get more long-winded, and my mind starts to wander after listening to a certain threshold of Ti, or if it's just a coincidence--too small sample size.
I do have Gulenko's latest book. I bought it before coming to CT. Maybe I'll go back to it and look if there's anything in it on these rings. XD