[T]he religion uses the ideology of pollution to ensure that women honestly signal their fertility status to men in their husband's family.I can imagine a variety of other explanations, however. For example, perhaps people who are more open to breaking with traditional norms and expectations are more likely to convert to Christianity or Islam than those who are not. The study examined 1,706 father-son pairs and found approximately 31 cases of non-paternity. If women who are open to extra-marital affairs are rare, and significantly favor an intrusive outside religion over the indigenous tradition one, the same effect would be observed. Perhaps women who aren't willing to put up with spending five days a month in an uncomfortable menstrual hut are simply more independent generally.
"When a woman resumes going to the menstrual hut following her last birth, the husband's patrilineage is informed of the imminency of conception and cuckoldry risk. . . .Precautions include postmenstrual copulation initiated by the husband and enhanced vigilance by his family."
It seems doubtful to me that public signaling is really that significant in alerting husbands to their wives's fertility, or that vigilance about something that all of the women presumably make a great effort to keep secret would really make that much of a difference between different religious faiths in the same ethnic community.
The conclusions of the study look to me like a case of anthropologists looking to exotic and flashy explanations for complex behavior patterns that may have more pedestrian causes.