You are using this concept of objective and subjective, which to me is irrelevant. Your example is that subjective is a preference, which does make a difference. Very few care as to whether I prefer chocolate to vanilla, including me. So what?
But we are talking about tastes. We are talking about morality. It does make a difference if I prefer to tell a lie rather than tell the truth. It does make a difference is I prefer to cheat and steal rather than honest work. It makes a difference to me, it makes a difference to those who come into contact with me, and it makes a difference to those who care a the well being of the social system.
Morality is not about preference. Morality is about good and evil. Goodness is that which harms people and evil is what harms people. We know that murder is wrong because it hurts people, however here is where the subjective and the objective do play a role.
We think we know what murder is, but it is not simply the killing of someone else. We know that there are 1st, 2nd, and 3rd degree murder. There is man slaughter and there is self defense. This does not mean that killing is good, but some killing is worse than others.
We need courts and trials to “objectively” determine the causes of killing, if those who are accused are guilty, and how serious the punishment should be. We might prefer that some one be found guilty, but we are a nation of objective laws that need to be enforced rather than our preferences, but our preferences are not at the heart of morality, but right and wrong. David was the clear favorite of God, but he committed adultery with Bathsheba and tried to cover it up by murdering her husband.