Their is personal possessive; they're might need a gender qualifier at some point but then again I'm just a truck driver.
Wouldn't a genderless driver be an it?
As in "This driver lacks confidence in it's driving abilities..."
smile)
I think the use of the third-person plural possessive pronoun has come about as a lexical figleaf, in response to fear of sounding sexist if one makes traditional use of the male pronoun intending it to be generic.
Although various new words for non-gendered third person pronouns have been proposed, none has taken hold. (Neuter, as you imply, doesn’t do it.) So people retreat to the relative safety of the plural instead.
No. “His” is genderless in this case and your use of the word “it’s” there is not correct either. No apostrophe, please. (See Rule #2 here.)
http://www.apostrophe.org.uk/