[Serious] Please convince me gender is binary

[bennyboy]

I guess that depends on the "we" in question. OK I agree with your statements. As to the OP though, I'm still not convinced gender is non-binary. I might start saying gender is bimodal  instead though.

Gender is compound trait assembled from a number of different underlying characteristics.

Some of the typical underlying characteristics used, such as genitalia, do have a continuous but heavily bimodal distribution.  Others characteristics that may be used have a shape that has not been so well and uncontestedly defined.    The selection of characteristics that goes into construction of compound trait is by no means universally agreed, not their relative weights uncontested.

“Conservatives” like to conserve what they conceive to be the correct final shape of the final trait, and would then cherry pick the characteristics and their weights so as to claim the a priori determined correct shape is not without basis.

1)  redefine gender using multiple axes which when evaluated collectively will not be bimodal
2)  subsequently claim that gender is non-binary

That's fine, but the fact is that the human species consists of people who are almost exclusively identifiable as male or female, both in physical phenotype and in their behaviors, both instinctive and learned-- and then there are those other people who either physically or psychologically have found themselves in a different place.

I don't think we need to take those 0.1% and make our entire cultural semantic revolve around accommodating demands.  There's too little payoff for the tremendous amount of energy that requires. So long as all individuals are protected legally from violence, from discrimination in the workplace, and so on, okay.

But I'm sick of hearing stuff on talking-head shows like, "If you don't use my pronoun of choice, that's an act of VIOLENCE. You are verbally assaulting me by calling me 'he' just because I have a penis, have XY chromosomes, and my parents named me Jonathan!"