How would the consequentialist and the non-consequentialist respond to reporting child abuse without clear proof, just out of "gut" instinct.

The non-consequenialist reports , or does not report, without thought or care of the consequents to those involved.
The consequenialist labours in deep thought over the consequents to those parties, with either outcome: whether the abuse is true or untrue.

The consequentialist and non-consequentialist ethical frameworks approach the situation of reporting child abuse based on different principles.

A consequentialist would primarily focus on the potential outcomes or consequences of their actions. In this case, if a consequentialist believes that there is a reasonable chance that child abuse may be occurring, they would likely err on the side of caution and report the suspicion. They would consider the potential harm caused by not reporting if the abuse is indeed happening, such as the pain and suffering endured by the child. However, if the consequentialist is unsure about the abuse and reporting it could lead to negative consequences, such as false accusations that harm innocent individuals, they may also consider those potential outcomes and weigh them against the potential benefits of reporting.

On the other hand, a non-consequentialist would focus more on the inherent principles or rules that guide their actions, regardless of the potential consequences. Although reporting a suspicion of child abuse without clear proof may go against the non-consequentialist principle of requiring sufficient evidence before taking action, the non-consequentialist may also consider the moral duty to protect the welfare of children. If they believe in a strict adherence to reporting any suspicion, regardless of the potential consequences, they would report the case.

Overall, both frameworks have different considerations when it comes to reporting child abuse without clear proof. The consequentialist assesses the potential consequences of their actions, while the non-consequentialist may prioritize their adherence to ethical principles or duties, such as protecting vulnerable individuals.