On a rainy September morning, a pair of cattle ranchers browsed the refrigerated meat cases at a Walmart Inc. store in Mandan, N.D., snapping cellphone photos of an unwelcome invader among the shrink-wrapped ground beef: Beyond Meat Inc. patties, made from pea protein and coconut oil. After a separate check at a nearby local supermarket, the ranchers headed to the North Dakota Department of Health. They showed officials the photos and warned of food-safety risks from mixing plant burgers with the traditional beef kind.

Their...