Objectivity and subjectivity aren't necessarily mutually exclusive. Subjectivity means you experience a moral sense. But there is still plenty of objective truth behind morality: DNA, brain structure, environmental conditions and so on.
You can both say, "I cannot imagine allowing a child to be harmed," and also identify brain structures and processes involved when someone thinks about the protection of young people.
You can both say, "I cannot imagine allowing a child to be harmed," and also identify brain structures and processes involved when someone thinks about the protection of young people.