It isn't clear to me that a definition that includes the word "normally" is effective in a context that involves an uncommon subset of persons.
For example, suppose we were having a discussion about a lesbian teenager. Someone writes, "define female." and you respond with "of the sex that is normally attracted to males." That isn't at all effective in context.
Now perhaps you could change the wording of your definition and it could be more effective. I don't know. I'm not over-analyzing it. Or perhaps you could try again.
As far as I am concerned, when people say "sex is binary," I think they are wrong and when people say that sex is fluid I think that is also an over-simplifcation. To me, and I could be wrong, sex has multi-dimensional characteristics, not merely one, and some of these characteristics may be fluid, binary, or bimodal, but overall, I think that sex is bimodal.
Transgender people are not an uncommon subset when it comes to the biological aspects of sex. There are vanishingly few transgender people who are even a tiny bit intersex. They are nearly all perfectly normal specimens of either male or female human biology.
Aside from that, I'm actually using the definition of female that biologists use, so you sticking a made-up hypothetical definition based on sexual orientation is irrelevant. Why not go that step further and take it upon yourself to define female as "likes tangerines and tap shoes"?
And you can believe whatever baseless belief you want... but sex is binary among humans, among all mammals, and among the vast majority of vertebrates. Literally binary. There are only two options: male or female.
Characteristics associated with sexual dimorphism show great variety. Boobs vary in size and shape, so do penises. And sometimes there are development disorders that affect primary or secondary sexual characteristics. But sex itself is binary, not bimodal.
Primary sexual characteristics are reproductive organs. They are binarily dimorphic along sexual lines, but sometimes errors occur during development. Size, shape, etc. of those organs show a range of possibilities, but they are not bimodal. There's no in-between state of half uterus half vas deferens. There is no overlap.
Secondary sexual characteristics are those triggered at puberty. These are naturally dimorphic and predominantly triggered by hormones, on instructions governed by the pituitary gland. These characteristics differ by sex, and if functioning properly do not have overlap. However, as they are triggered by hormones, processes that interrupt or alter hormone production can cause the development of secondary sexual characteristics that are associated with the opposite sex. That includes the effect of exogenous hormones. A female taking testosterone will develop facial hair. A male whose testosterone production is interrupted by an intersex condition may develop breasts.
Tertiary sexual characteristics are those that tend to cluster by sex, but those ARE bimodal and are not dimorphic. Thus, males generally tend to be taller and have larger hands and feet. But while it's uncommon, it's not rare for some females to reach heights in the normal male range and have large hands and feet.
Sex itself, however, is not defined by sexual characteristics. Rather, those sexual characteristics are
prompted by sex. And sex is binary. The chromosomal pairing that generates a fertilized egg dictates the development of gamete production organs. And there are only two gametes. No third gamete exists among humans, nor among all mammals. No in-between gamete exists. There are two, and only two, gametes.
