This is my first patch, be nice.
This is only for fixing edit mode X-Mirror. I'd also like to fix pose mode X-mirror, but I didn't want my first patch to be too big. Therefore this is only a partial fix for T65671.
I also don't know for sure if I'm adding all the appropriate update functions in all the appropriate circumstances using RNA_def_property_update(). But everything seems to work fine when I'm playing with it.
Slightly long video showing the fix in action: