In reality, morality does not even exist (except as a concept necessarily contingent on a conscious mind).
I agree with this quote with regard to moral obligation.
Therefore, I think morality is primarily subjective. But I also think morality is relative. And I think that morality is objective.
How do we get objective morality from subjective morality?
Consider the following:
Subject A believes it ought to be wrong to do action X.
Subject B says, "Subject A believes it ought to be right to do action X." Subject C says, "Subject A believes it ought to be wrong to do action X."
In the above situation, it can be said that Subject B’s statement/opinion is incorrect while Subject C’s statement/opinion is correct (factual), objectively speaking. Even though Subject A’s opinion of the state of moral obligation regarding action X is subjective, it still exists independently of Subject B and Subject C. While it’s true that Subject A could change her belief, it is still a truth/fact that is independent of the minds of Subject B and Subject C.
What about morality being relative?
If Subject A obtained sufficient power (authority) to declare action X wrong and has the ability to enforce that declaration, then action X is also wrong for whoever is under the authority of Subject A. Meanwhile, action X remains morally undefined for those not under Subject A’s authority.
Take driving for example. In the interest of safety and efficiency, is has been decided that American drivers will drive on the right side of the road. Driving on the left side of the road has been declared wrong due to it jeopardizing lives. However, driving on the right side of the road is wrong relative to if you are under the authority of the United Kingdom.
Relative morality doesn't have to be formalized in written law either. Action X could become generally accepted as wrong by a society. And that opinion can be enforced and passed on via group-think.
Now, take Subject God.
God can believe that it ought to be wrong to do action X and has sufficient power to declare action X to be wrong. While it’s true that it is His subjective opinion, it’s still objective to anyone who is not God. God also has sufficient authority to declare action X as wrong and enforce it.
Who is under God’s authority?
According to Christianity, all of reality.
The ancient classic... Is God’s opinion of action X arbitrary(1) or does God think action X is wrong because action X is wrong independent of what God thinks(2)?
Well, we already established that action X can’t have a moral stance independent of minds. Therefore, (2) must be rejected.
And (1) must be rejected because it leads to moral absurdities. Like saying that God could've commanded humans to hate Him instead of love Him.
How about option (3)?
If God’s character is the ground for the good ("good" is a value. It’s different from obligations like declaring action X is wrong. Examples of good values are; love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, and self-control ), then the good is objective because God’s character just is His character independent of His opinion of it. Therefore, God’s opinion of action X is not arbitrary, but is based on His perfectly good character.
So, in the end. God's commands are right because God has the power and authority to command them. And God's commands are good because God is good.