Artist Jess de Wahls and biologist Güneş Taylor play Spectrum Street Epistemology in London. They explored the distinctions between being female, being a woman, and identifying as a feminist. They also examined the concept of chivalry and its relationship to gender roles and expectations.
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NO.
Allow me to elaborate on why NO is the answer and how it doesn't change based on any additional criteria to the base question.
Base Q: Should we treat men and women differently
Additional Criteria: if gender is a spectrum
Regardless of "if gender is a spectrum" or any other criteria, men and women are not the same physically, mentally, psychologically or emotionally. Trying to treat two different sexes the same is like trying to use the same solution to every question, the same fix to every problem.
"Should We Treat Men & Women the Same if Gender is Truly a Spectrum?"
Kind of a clueless if not pretentious question -- a "deepity". Apparently predicated on ignorance of more or less standard definitions for both sex and gender. Sex is, by definition, a binary, and membership in the sex categories is based on having functional gonads of either of two types, those with neither being, ipso facto, sexless. See:
https://academic.oup.com/molehr/article/20/12/1161/1062990 (see the Glossary)
https://link.springer.com/referenceworkentry/10.1007/978-3-319-16999-6_3063-1
https://twitter.com/pwkilleen/status/1039879009407037441 (Oxford Dictionary of Biology)
As for "gender", it is, at best, no more than a synonym for a range, a spectrum, of sexually dimorphic personality types, behaviours, roles, and modes of expression. See my post for details:
https://humanuseofhumanbeings.substack.com/p/a-multi-dimensional-gender-spectrum
But Merriam-Webster put's it quite succinctly:
MW: "gender: 2b) the behavioral, cultural, or psychological traits typically associated with one sex"
https://www.merriam-webster.com/dictionary/gender#usage-1
Do note the "associated with" -- i.e., not intrinsic to either sex, only typical of. How we can have masculine (gender) "adult human females" and feminine (gender) "adult human males".
But to answer your question, that a man -- i.e., an adult human male -- and a woman -- i.e., an adult human female -- might be at the same ends of one or more dimensions of gender in absolutely no way changes the brute fact that one is a male and the other is a female. Of course they should be treated differently -- for one thing, sexual reproduction might be somewhat "unlikely" otherwise.