Actually I would be in favour of the introduction of a set of universal 3rd-person-singular pronouns that come to be used for all humans regardless of gender/sex. We can still know who the men are for the purposes of privacy, decency and fairness and no one should have to declare their gender beliefs for normal human interaction.
I don't like using singluar they, although I will in some circumstances, but a pronoun is supposed to fully substitute for the name in a sentence.
"Please can you ask Peter if Peter eats chocolate cake and if Peter wants sugar in his tea when Peter comes to visit. I think Peter has a sweet tooth, doesn't he?""
Maps directly to
"Please can you ask Peter if he eats chocolate cake and if he wants sugar in his tea when he comes to visit? I think he has a sweet tooth, doesn't he?"
- the pronoun replaces repeated instances of the name but no other grammar changes.
However if you use They/Them it's
"Please can you ask Ziam if they eat chocolate cake and if they want sugar in their tea when they come to visit. I think they have a sweet tooth, don't they?""
- all the verbs have started taking plural forms so the pronouns are not doing the job correctly.
If we adopted a universal unisex pronoun then you could say
"Please can you ask Peter if ze eats chocolate cake and if ze wants sugar in hir tea when ze comes to visit? I think ze has a sweet tooth, doesn't ze?" - and then it is doing the pronoun job correctly and the sentence is exactly the same if the person referred to is Anne or Ziam
I would like this because while I don't mind using they/them occasionally, I construct my sentences very carefully to avoid having to use opposite-sex pronouns which feels like lying.
When Ms became popular as a title I liked it because shops and other businesses really don't need to know if a woman is married or not to do business with her, especially when they don't ask a man.
In a similar way, I don’t think we should be centring our belief or not in anyone's gender identity if we are just referring to them in casual conversation unrelated to the entirely legitimate circumstances when their sex is relevant and important. Starting to use ze/zir for everyone regardless of gender identity or absence thereof would achieve this, in a similar way to addressing a female teacher as Ms Smith by default without checking if she'd technically be Mrs or Miss.