It's not what I had expected:
Observing an old and curious Navajo taboo, Narbona was not allowed to look at his mother-in-law, nor she at him. It was a custom designed to keep the peace and, apparently, to avoid sexual tension. In fact, many mothers-in-law in Navajo country went so far as to wear little warning bells on their clothing so that a son-in-law would not round a corner and inadvertently find himself staring at her. This was no small thing, especially if he happened to look her in the eye. Even an accidental violation of the mother-in-law taboo might require that the family hire a healer to perform an elaborate -- and expensive -- nightchant to undo all the harm that had been done.
That is from Hampton Sides's quite interesting Blood and Thunder: The Epic Story of Kit Carson and the Conquest of the American West. From the specialized academic literature, here is an entire study of the mother-in-law taboo (JSTOR); I'm not sure any of the offered hypotheses or explanations are persuasive. It seems the taboo lasted well through the twentieth century. Here is another discussion, under the more general heading of Navajo taboos:
The only explanation ever given for this custom is that “it avoids a lot of trouble in the family.”