in my experience

Sure, it's quite possible that people have a stable preference for dominant/submissive behavior in social interactions. I think that's a fairly uncontroversial thing to posit.

The problem with the Blue team is that it ignores the underlying mechanisms

That's probably because the "Blue" side is not actually a monolithic, self-aware school of thought. "Blue" is an exonym created by Red to describe the amalgam of conventional wisdom and pop-feminism to which they construct themselves as opposing (analogous to how "Cathedral" is not a monolithic, self aware group, but an exonym created by reactionaries). In reality, pop-feminism and conventional wisdom doesn't often bother delving into evo-psych and thinking about sexual strategy...so the seeming lack of specificity inherent in "click" is not in opposition to anyone, but simply the result of not having adopted a position on the matter.

The problem with the Red team is that it treats individuals as fungible: provide the right signals and it doesn't matter who your partner is

Well, personally I think the additional, and more pressing problem with Red is that it is factually mistaken in its conclusions about what sorts of signals one should send out and how these thing work.

it seems reasonable to me that for a successful relationship people do need to "click" together (Blue), but whether they do click is determined partly by what they are, what image they present, and what signals they send out (Red)

What you described there is not a spectrum from Blue to Red. Blue to Red would look something like "attraction is about signalling affection and kindness" vs. "attraction is about signalling dominance and demand".

What you describe is a spectrum from Black to Red, where Black is the absence of ideas about attraction and sexual dynamics -"something" happens and it just clicks - whereas Red/Blue is a specific position on what that "something" is. The difficulty with distinguishing Blue and Black arises because the whole construct described by the term Blue is partly real conventional wisdom and partly a Red straw-man.

And there's no reason to a priori assume that Red or Blue is actually correct* about what general signals you aught to send out to induce attraction in the average, generalized case, nor is there reason to assume that the truth is anywhere in the middle of these two. There might be a third, Green position which captures the fact of the matter.