I work hard at tolerating singular they, I really do. but if you're going to use it, ought you not try to be internally consistent with, like, objects?! here's a jarring (to me) example of a failure to do so:

..each was expected to present a short report on highlights in their respective bureaus[!sic!] since last weeks meeting. - John Lescroart, The Second Chair

I can imagine this to be the work of a lowly copy editor, but still. (if this has left you scratching your head, try substituting an actual singular pronoun such as his or her for their in the example.)