They are both nuisance species—native plants and animals that can cause problems. According to the Missouri Department of Conservation (MDC), the Osage orange tree “can become a nuisance in prairies and savannas. It also invades forest communities, usually as a result of past disturbance, such as grazing.” Lots of deer can “damage crops and ornamental plantings and increase the potential for deer-vehicle collisions.”
In fact, nuisance deer in the city of Ladue were recently managed by a hunt.
You can read about other nuisance species on the MDC website: