Moral relativism equates to endless justification for any action. Moral objectivity exists; outside of outliers, humans in general share a common theme of camaraderie and cooperation among one another in the same 'group' or 'tribe'. That's part of why Jesus instructs us to love everyone, neighbor and enemy, because then our natural goodwill is always extended to everyone.
Its not a matter of belief, but objective reality. To be clear, no one who studies math says "do you believe in X?" as you can verify and prove concepts objectively. The reality however is that when we are asking what something is or isn't, what we should or shouldn't do its easy to get muddied down if we don't know what we are defining or know where we are trying to go. In this case Morality, meaning right and wrong behavior exist and must be exercised honestly and understood.
The reason people have differing opinions is because of different taste or wanting there to be a subjective aspect, because once you realize what you are bounded by the major question is "what do you do from there once you know that you know?".