We do not have trouble saying and writing "you" instead of "thee", even though the former used to be used only as the plural of the latter. In some cases, we use "we" instead of "I", such as the "royal we" or the "editor's we", even though normally "we" is the plural of "I".
So, why not use "they" instead of "he" or "she"? Why is that so terrible? We can use plural verbs with "they" even when we are using "they" as a singular pronoun, just like we do when we use "you" for one person. For the singular reflexive pronoun we can use "themself" much as we use "yourself" when it is just one person.
That's pretty easy and it is becoming common practice anyway. So, why keep complaining that it is wrong?
Copyright 2016, Lee Newberg. All rights reserved.