Most of this was answered in previous such threads.

And Collin said a bit different thing to what you are presenting he said. He said we are not typical male or female, not that we are neither.

Intersex is an umbrella term to a 40 very different conditions. All but 2 are happening only to one sex (and to be honest even those 2 are only visible on females). It is 0.18% of population shared by 40 conditions. Majority of conditions are unambigiously male or female.

Few where it is not that clear (like mine) are requiring few extra tests, to check:

1. Working gonades or gonade leftovers.

2. Genotype - SRY gene is checked (so XY without SRY can be considered female, as Y did no changes to organism and organism developed as female, but with some health issues).

3. Genitals.

4. Phenotype.

5. Natural hormonal level and hormonal sensitivity.

For few very rare conditions can be done some extra testings, but those are depending on specific person and are different each time.

For example, my condition is deadly if not treated after birth and males with females need different treatment, so when I was born with virilized body and enlargened clitoris, I was sent for screening, they found working ovaries and they gave me treatment for a correct sex, saving my life. And it happened almost 50 years ago in second-world country. Today healthcare is even better at this. Plus males and females have different complications and need different additional treatment (I got early Secondary PCOS and taking contraceptive pills to treat hormonal imbalace) - similar to all other people of same sex. And treatment needed by us is similar to other people of same sex.

Is intersex a disorder? Isn't it bigotry to call intersex people disordered or tell them they have a disorder? We mean something is wrong with them or their body, which sounds dehumanizing?

Why it is bigotry?

We all have health issues which require treatment. It is very important to know it and not ignore treatment and just saying "they are other sex and need no intervention" - will kill many of us.

And isn't disagreeing with transgender identities racist?

Transgender identity is not a race.

There have been many cultures that had a similar concept to transgender. They had third genders in these cultures, and that's where transgenders get their idea of gender identity from. Isn't it disrespectful to these cultures to disagree with transgender identities?

No. Transgender people of today are not from those cultures and not following those cultures standarts. "Third genders" there had no voice, were not allowed in female spaces, were mostly doing housewife job or were taking care of kids. Transwomen of today are not doing any of this. And transmen analogues did not existed until 20th century.

All those cultures were not saying that man becomes a woman. All those cultures were strongly patriarchical and those "third genders" were almost always homosexual, infertile or weak men. They were below men, but above women in social status. They were doing jobs meant for men and women, while regular men were not doing "women's housework". Very often those "third genders" were castrated or sterelized in other means.

Those third genders were always very homophobic practices. Like in modern Iran.

I am myself victim of similar practices - was put on testosterone to "cure" my lesbianism.

On the other hand - transgender activists exploiting and misrepresenting those cultures is racism.