What's that mean exactly, that they use proteins that can be further folded, and they exploit that property?

If we're being pedantic fungi have neither gender nor sex, they have "mating types". But yeah, mating types are more analogous to sexes than genders. Fungi would have to have some level of social experience to have gender.

Humans have more than 2 sexes. Sex is a convenient category based around a phenotype, not a golden rule that all organisms adhere to. People who exist outside those phenotypes are not defective or malformed and do not necessarily require surgeries to 'correct' their bodies and make them fall in line with binary sex categories.

The reason that science has been able to assert that sex is binary is by excluding all organisms that exist outside those phenotypes. Its a problem when those organisms are people, as you are functionally erasing their existence or at the least handwaving it away as irrelevant. This is one of the many vectors along which intersex people experience discrimination.

By asserting sex as binary and immutable you are actually doing the legwork of transphobia for transphobes. They also assert that sex is binary and immutable. They deny that any such thing as gender identity or expression exists in the first place, instead asserting that gendered behavior is a direct product of biology.

I am not a 'male woman', to even try and state that is to deny my own biology and experience. It is transphobia.

Not in my experience.

It's not even genders, it's a whole different type of reproduction. Sexual types.

Mushrooms do not have male and female sexes; instead, they have mating types, a system of genetic factors that determines compatibility for sexual reproduction. Unlike animals, fungi don't possess specialized organs for sex, but can have thousands of different mating types within a single species, allowing for broad reproductive compatibility and increasing genetic diversity.

Mushrooms must look at us like we look at monocellular life.