It was a bit glib, but I enjoyed writing the following footnote in my chapter. There is little as satisfying as producing a solution to a problem of style with an actual thought:
I will employ a masculine pronoun for “the” ethnographer, for reasons of convenience as well as a reminder of how structurally gendered the scientific gaze of this figure is, informing, in turn, the terms in which it becomes possible for “him” to write about gender in traditional culture.
That said, I find I have no qualms over the use of “their” as a way to sidestep the “his or her” thing; breaking a minor grammatical rule seems preferable to the other options, each of which sacrifices something good. “Their,” on the other hand, gives us what the English language needs, a gender neutral pronoun.