I fully agree with your sentiments and would never use a singular "they".
But there are two approaches to teaching language: the prescriptive and the descriptive. Mostly we here at Usingenglish are descriptive. Changes in language are like locomotives; their momentum is so immense that nothing can stop them. Changes that we may personally detest are here to stay, so we usually confine ourselves to understanding and describing them, because railing against them is pretty much useless.
That is the best way to serve our students, who are not native speakers but have to cope with those government forms and letters you mentioned.
Interested in Language