A wealthy person donates thousands of dollars to charity, not out of generosity but in order to save on taxes. Which kind of ethical theory would maintain that the motives here would not matter so much?

The teleological theory would maintain that the motives won't matter so much.

Explanation:

The teleological theory comes into force when the motive behind the action is not something that inspires the action, rather it is the cause of the action that the action is inspired by. In the given example, it is clear that the wealthy person is not doing it utterly for charity but for the purpose of tax evasion which is not an ethical act. Hence, his act is not justified and can be termed as unethical.