Which ethical system is most likely to support the harassing and inconveniencing of a racial minority group because it being done in the pursuit of a justifiable goal such as preventing terrorism? ?

The answer to this question is a utilitarian system
a utilitarian system is an ethical theory that believe the best course of action is always the one that give the maximum utilities
Through this ethical system, a country might decide to invade another country that been accused of spreading terrorism because they know that they will reap long-term benefit from the invasion (by taking resources)

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