If we take the heading at face value:
"If you don't know someone's (1) gender (2) or when talking about a group, use (3) gender-neutral (4) language"
(1) If you DO know "someone's gender" : (an individual, not a group)
Humankind - mankind - womankind
could all be appropriate depending on the meaning
eg. "she was the epitome of womankind" rather than "she was the epitome of female members of humankind" (how poetic!)
Chairman - Chair
"Convenor" is a well-established alternative in some parts that avoids the clumsiness of "Chairperson". "Chair" is fine but the UN is dictating (3), not suggesting.
Congressman - Legislator
"Legislator" would be insufficiently specific in some contexts (this is supposed to be about referring to a specific individual, not a group).
Businessman - Representative
Bizarre, nothing to do with "gender" and makes no sense unless the aim is to change understanding of the role of Business in relation to the public. Who/what is being "represented"??
Imagining Newspaper Headlines:
"Local Businessman . . "
"Local Businesswoman . . . "
"Local Representative . . " (of what?)
"Local Business Representative . . . " (a local representative of "business"? a "representative" of a local business?)
Policeman - Police Officer
As mentioned above, there are occasions when it is important to know the sex of the Police Officer.
From a feminist perspective, the move to use of "gender neutral" language has both upsides and downsides.
One of the downsides is that it over-rides the principle of "equal but different". Women as a group become invisible. The importance in some contexts of sex-difference is eroded.
Was there any need to remove the Job Title / Rank of "WPC" in order to ensure equality of pay, status, etc. between male and female? (Just thinking aloud.) In practice, where sex is relevant then "woman", "female" or "male" are often used in conjunction with "Police Officer".
Which is a good illustration of how messy the English language is in real life: ever heard of a "Man Police Officer"?
Landlord - Owner
Already done to death in previous posts. I read "Landlord" as meaning "Publican" so found this one very odd until I saw comments on it!
Boyfriend/Girlfriend - Partner
Cloth-eared beyond belief! See PP above.
I am getting bored with that now!
(2) "Gender" : Or do they mean "sex"?
(3) "Use" : How very dare they! Eff' off with the compelled speech directives!
(4) "Gender-neutral" : just gets my hackles up every time I see the bloody term these days.
More seriously . . . there are circumstances in which it is useful to specify a restricted vocabulary. If this was the intention then "UN Women" should have made this clear, though why on earth "UN Women" should think it their business to dabble amateurishly in this area is another thing.
The example I remember is "Caterpillar English" but there are other examples of "Controlled Natural Language (CNL)"
"This is the website of the special interest group on Controlled Natural Language (CNL).
Controlled Natural Languages (CNL) are languages that are based on natural language but apply restrictions on vocabulary, grammar, and/or semantics. Some CNLs are designed to improve communication among humans, especially for non-native speakers of the respective natural language. In other cases, the restrictions on the language are supposed to make it easier for computers to analyze such texts in order to improve computer-aided, semi-automatic, or automatic translations into other languages. A third group of CNL has the goal to enable reliable automated reasoning and formal knowledge representation from seemingly natural texts."
www.sigcnl.org
I would hope that people who actually specialise in this sort of thing have a better handle on the subject.
If there are any Mumsnetters on FWR who are Linguists then maybe they might be motivated to check it out?