Let me start with some premises.
1. God, or some kind of higher moral authority, is necessary for objective morality to exist.
2. It has not been proven that God exists. For those who currently do not believe in God, there is no particular reason why they should change their mind on the issue.
3. Therefore it's likewise not been proven that objective morality exists and for those who don't already believe in it, there is no particular reason why they should.
Therefore if a person claims that a certain moral position is objectively true, there is no way for that person to prove that it is so it effectively is no more valid than any other moral claim, whether it is claimed to objectively true or admittedly subjective, so the claim of moral objectivity, even if it happens to be correct, effectively adds nothing to the claim and therefore is effectively useless.