Without turning this into a Groundhog Day of First Principles . . .

Why doesn't intersexuality show that sex is a spectrum and not a binary in humans, and that sex is not immutable and can change?

Numbers. You can literally stop there with all academic honesty intact.

And is sex determined by phenotype or genotype?

Genotype. That's how human genetics works.

If sex is determined by genotype, then why don't chromosomal differences show sex is a spectrum and not a binary?

Numbers. The rare exceptions (and there will always be exceptions) do not eclipse the general rule.

what about intersex conditions in which someone with xy chromosomes has no testes but develops testes later on (e.g. Guevedoces)?

A very localized and genetically circumscribed phenomenon. It doesn't eclipse the rule.

What about intersex conditions in which a male has a womb and fallopian tubes? (e.g. Persistent Müllerian duct syndrome)

A very rare developmental disorder.

How can they be male when they have female sex organs?

How can a person be a human mammal with a laterally rotated heart (LA/LV on the right, RA/RV on the left)? Two spleens? Redundant musculature?

Exceedingly rare genetic mutations and expressions and in-utero developmental events, none of which are the rule.

Negation of rules by highlighting rare variants and exceptions -- not a great strategy. It's not remotely how science works, let alone very basic biology.

(ETA I have known people irl with a laterally rotated heart, two spleens, and redundant musculature. No clownfish were harmed in this analysis.)