https://phys.org/news/2018-07-gamekilling-rabbits-native-mammals.html

Food webs are complex. Because of this, once an invasive species is embedded in a food web, simply eradicating them without considering the potential knock-on effects to other species they interact with, could cause unintended and undesirable consequences. We modelled different rates of rabbit population reduction to assess what level of control might be best for aiding the conservation of native mammals and not causing negative outcomes.

Rabbits, famously, reproduce rapidly and can cope with a relatively high predation rate. This can cause "hyper-predation", where rabbit-inflated cat and fox populations indirectly increase the predation pressure on native mammals. This is especially so when rabbit populations intermittently crash due to, for example, extreme environmental events (like severe and prolonged droughts) or disease. This causes predators to switch their diet and eat more native mammals.