Context: When discussing with Gender Propagandists who claim over 100+ genders exist, they always tell us that biological sex isn't a binary either. This is far from the truth, however they ask us to define what it is, so this short post will answer them:
The best way to define it is based on the body's attempt to create gametes. Some people can't create gametes, but their body is based around ovaries (female gametes) or testes (male gametes). In most cases chromosomes dictate which gamete you can produce. There are some cases of intersex where that isn't the case, but in the end, their gamete production determines the sex. Chromosomes are accurate for 99%+ of people. Attempted gamete production is accurate for every living person. And it always falls into male or female, except for "true hermaphrodites" who are potentially both male and female. However, it is also possible even true hermaphrodites can only produce one gamete. No true hermaphrodite has both fathered and mothered a child. But some have fathered a child and some have mothered a child. So, thus far in human history everyone has been either male or female as far as we know, not both.
No such thing as "true hermaphrodite" in humans, OP. Even the term "pseudo hermaphrodite" that previously was sometime used has fallen out of favor and now considered bad form when speaking of humans.
People with DSDs, clinicians who treat them, and researchers who study them and their conditions long have asked the world not to use the term hermaphrodite, true or pseudo, when speaking of humans with DSDs. Because it's not only othering, it's monstering and stigmatizing.
The potential to create male or female gametes at some point in the life cycle after sexual maturation is what defines sex, not "the body's attempt to create gametes" or "gamete production." Embryos, fetuses, babies and children prior to puberty of adolescence cannot generate fully-developed gametes, but they all still have a sex! Everyone is male or female long before reaching the age when the body will "attempt to create gametes" and will be able to engage in "gamete production."
Similarly, women after menopause are still female even though our bodies can no longer produce gametes, and in fact no longer even attempt to do so. Menopause doesn't make women sexless.
Actually, the traditional view is that only the sex chromosomes determine which kind of gametes a person will have the potential to produce. The sex chromosomes are just one type of chromosomes.
Moreover, what really dictates gonadal sex and thus potential to generate gametes at some point in the life cycle after reaching sexual maturity is the presence or absence of the SRY gene that's usually on the Y chromosome.