If one accepts a form of consequentialism, this implies that they should select actions so as to make the world as good as possible, according to their values, and disregard any other considerations. "Neutrality" is this disregard for non-consequentialist considerations.

Suppose you value the welfare of all humans equally, and suppose that dementia research is not the most effective way to help humans. Then being neutral means you should not fund dementia research, even if dementia has personal significance to you (e.g. because it affected a family member).

Note that the implications of neutrality vary with the value system that one holds. If the person in the above example instead placed special weight on the welfare of those suffering from dementia, then supporting dementia research might actually be the best course of action....

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