Sorry. Not buyin' it.The meaning of 'man' has changed in recent times
The meaning of words do not change just because some people want them to. The words "man" and "mankind" are still quite widely used and still quite acceptable with their "traditional" meanings.
Besides, those words have never been meant to be any kind of affront to women, and pretending they have is nothing more than politically-correct posturing.
I sympathise.
My personal bugbear is the American tendency to replace the term “I couldn't care less” with “I could care less”, which is absurd.
But the fact is that meanings and interpretations of words evolve and change, quite often coming to mean the exact opposite of their original definition. Off the top of my head, the following words no longer mean what they once did and the commonality or otherwise of their usage reflects this gradual change:
Gay
Negro
Terrific
Fulsome
Awful
“Authoress” is no longer in common usage to describe a female author, yet “actress” is still more popular than the generic alternative - “actor”. Why?
Since 1989, some terms have become almost useless as a shorthand conveying of one's overall political/ideological outlook in much of the Anglo world:
Left wing
Right wing
conservative
liberal
Only “communist” and “fascist” retain some of the power of meaning they once held, and yet because of their widespread use as a form of personal abuse in the bloggers-sphere, they too are beginning to lose impact. “Zionist” is increasingly used in this way. Interestingly, its originally secular meaning has also changed so as to be commonly used today as a descriptor of religious Jewish Israelis.
Patrick Stewart has always been more than happy to describe himself as a “socialist,” and this is still generally a positively understood term in western Europe. In the USA, it is almost interchangeable with “communist.”
“Fundamentalist” is today a term of abuse while progressive” is being adopted by the hip-and-happening-crowd.
Long story short, the English language is a mongrel, constantly adopting and adapting foreign words and phrases, tipping long-standing meanings of English words on their head, and it's consequently all the more dynamic.
I personally favour “no one” to “no man” in the Trek intro, but what counts as far as the English language is concerned is which of the two is more generally received and becomes common usage. I'd suggest that time is beginning to tell.