There are no true human hermaphrodites (people who produce sperm or egg). Sex is based on the type of gamete that your body is built to produce, sperm or eggs. This is strictly binary. There are no speggs or alternate gametes. All humans with DSD's (or intersex people) have bodies that developed to produce one type of gamete or the other, but something got messed up along the way. The majority of DSD's result in sterility and often other systemic health problems as most developmental disorders that cause odd-looking genitals also cause other issues in the body. I.e. People with AIS have low-bone density and are at greater risk of fractures, people with CAH have trouble regulating electrolytes. People with DSD's are not a third sex, they are either male or female with developmental defects causing them to look or function differently.

Think about it this way: Humans have four limbs with five digits on each limb, right? Well sometimes people are born with extra toes or fingers, so should we say that there is a spectrum of limb-types? I have a relative with a missing heart chamber, so should we say that humans have a spectrum of types of hearts?

The fact that there are non-human animals where true hermaphroditism exists (i.e. clownfish are sequential hermaphrodites) has nothing to do with how humans should build our society around sex. The variety of sex developmental systems in nature is endless and fascinating but just because its possible in clownfish doesn't make it possible in humans. Clownfish can truly change sex (M to F) as in able to produce the gametes of their new sex. Salamanders can regrow limbs. Zebrafish can regrow their hearts. Male anglerfish physiologically merge with a female and become nothing more than a pair of testicles, with no fins or brain. Whiptail lizards are an all female species that reproduces via cloning that engages in sexual activity anyways. Humans can't do any of these things, so it shouldn't have any impact on discourse on how human society should work.