Sometimes I think people are just out to make difficulties.
I mean, what's wrong with this?
God send everyone their heart's desire.
...if ye from your hearts forgive not everyone his brother their trespasses...
Every body has their level.
The answer? Well, as the first is Shakespeare, the second the King James Bible, and the third Jane Austen, the answer plainly must be ABSOLUTELY NOTHING AT ALL.
And yet people will insist that you can't use their to mean his or her.
The thing is, we need words in English for his or her and he or she: but although we've had words for both for centuries - their and they - some people just won't have it.
Some mad people have even gone to the effort of making up new he or she words for us: we've been offered, amongst others, mon, heesh, ho, et, hir, jhe, na, per, xe and po.
Strangely enough none of them has caught on.
Personally, if a singular their is good enough for Shakespeare, the Bible and Jane Austen...
I must admit I've never dared put one in a book, though. Not deliberately, in any case.
Thing To Do Today: use their as a singular - and quote Shakespeare at anyone who gets sniffy!