I work hard at tolerating singular they, I really do. but

Oh, pshaw! As a feature of English grammar, from some of our best writers, for over six centuries, it should not only be tolerated but taught in grammar schools.

[!sic!]

What abomination is this? Does this mean "not sic!" or "not sic not"?

Anyway, I see what's going on, and it's interesting. Obviously, their still retains a trace of plurality, and therefore, the plural on bureaus (erm, bureaux) seems right. If I penned the sentence, though, I'd probably go with the singular bureau as well as the singular they.

Ceci n'est pas un seing.