I have been told that dichotomous/binary traits are actually very rare or don't exist.

A dichotomy is a mutually exclusive or oppositional difference between two things. Female and male aren't dichotomous, they're dimorphic (having two distinct forms).

the "law of the excluded middle" that requires the contrivance of making up fallacious dichotomies, and binaries, when in reality there are complex continuums

Contrast with taxonomy and biological categories, which are based on consistent categories of observables, not an excluded middle or overlap. Human sexes are two distinct categories and conform very reliably to female and male; exceptions are exceedingly rare.

Also, taxonomy is not a logical fallacy. It's an empirical organizing principle.

Who decides where to draw the line? And how can we trust that line?

We decide where to draw the line. That's why we invented science. We can trust that line through the consistency of proof. Science has consistently proven that humans are sexually dimorphic. This is a very stable understanding.

Humans share 50% of their genes with bananas.

Humans and bananas are also both carbon-based, capable of reproduction, and exist on the planet. Which comparables are we talking about here?

That means there is no such a thing as a human/animal, plant, or anything else?

No. It means there are categories of things constrained by consistently predictable qualities, and their qualities are so consistently predictable we can give them distinct names.

Are we distorting actuality to fit the pattern of language? Language creates all these discrete categories, where someone or something is either a certain type, or not that type at all.

Language does not create discrete categories. We create discrete categories based on given qualities (in science -- on concepts of empirical observables) and invent language to describe those concepts.

Whereas reality tends to follow the pattern of fuzzy logic i.e. fuzzy set theory, where there are degrees of membership, and where something is not in one discrete set or the other:

Where does degree of membership begin and end with a banana? If it contains a high degree of citric acid, is it still a banana? If it grows on a moist rock, is it still a banana?

You're mixing together various concepts from philosophy, linguistics, mathematics, biology, and rhetorical strategies (logical fallacies) in an attempt to prove that reality is mutable beyond the point of creating categories at all. The organization of knowledge doesn't quite work that way.