I'm a gender atheist too (I love that, i think its better than gender critical)
I think gender is how society responds to an individual based on their presentation of characteristics or behaviours statistically, historically or socially more likely to be associated with one or other biological sex (sex stereotypes). I don’t think it is binary, bimodal, or a spectrum. I just think it is irrelevant, divisive and reductive.
biological sex (Male/Female)
I think that biological sex is a pure genetic binary (all chromosomal disorders can be accurately placed into the binary, based on the presence of absence of a Y on the 23rd pair, and if development proceeds properly gametes of either egg or sperm are a reliable indicator of that).
primary sex characteristics (Man/Woman)
I think that primary sex characteristics are also biological (genitals and small heritable evolutionary brain structure differences such as INAH3 size and density) are bimodal in distribution (with the tiny overlap caused when foetal development doesn't go smoothly due to prenatal hormonal exposure(a) and congenital conditions(b)
*I believe (and I know this will be controversial), that pre pubertal onset homosexual trans folk fit in here as per the research by LeVay,1991 and Dick Swaab, 2008 and so truly do have rights to the title man/woman, so it is my belief that the Gender Recognition Certificate should be much harder to get, maybe even be screened for in infants but give full access to sex based rights and recognitions.
*I think people with Developmental sex Disorders/intersex conditions are very rare and are treated as individuals based on the developmental condition. My understanding is that these are finite and well understood, they are a bit sick of being drawn into the trans debate, that the clinically assigned sex is nearly always correct for the individual except in a couple of notable conditions(complete or severe androgen insensitivity and 5ARD) but that the individual should be entirely free identify however they choose.
Secondary Sex Characteristics
( breasts, muscles, Adam's apple, high/ low voice, levels of aggression, physical size, pelvic width, facial feminisation / masculinisation, some brain changes, some behaviours e.g. submissiveness, dominance, aggression, sex specific fetishes and paraphilias)
I think secondary sex characteristics are biological and dimorphic (proceeding from the hormonal influence of biological sex during puberty. Each characteristic has its own bimodal distribution but many of them are chemically or cosmetically “fake-able”.
Social characteristics and behaviours
(clothing, makeup, mannerisms)
This is the realm I think adult onset, same sex attracted trans women with menstruation fascination come in (and non binary folk with no dysphoria).