WARNING
Morality, whether absolute or relative, always lays down a law. It demands adverse consequences for those who defy.
Even to say that morality is relative is to rule that morality is what we want it to be.
Many reply that you cannot live without power in some form - you have to control. They say that that has risks but letting people control you with an invented morality is totalitarianism and totally foolish.
THE ARGUMENT
People tend to oppose those who say that moral laws are whatever they say they are. They include versions of God where God claims this power. They worry about the principle, "Even if it would never happen, we don't want to think that just because x says we may kill babies for fun that it becomes morally right or morally tolerable." And they worry about the consequences. People or their God will try to make harmful things right.
So they worry more about having a morality that does not imply or lead to what is arbitrary - even at the expense of the morality being accurate.
For that reason, many believers limit the right to decree morality to God alone. That solves the arbitrary problem they say. Even if it does, it does not solve the relativist problem. A relativist morality that is dished out by one being, God, is still a relativist morality.
Objective morality should be unchangeable but a relativist morality can claim to be unchangeable too. Unchangeability is not enough to make a morality objective. Many of those who say objective morality is grounded in God, could actually mean relativist morality.
If you are a moral relativist, there is no problem if you want to claim there is an objective morality - you can do that as a relativist. On relativist grounds, lying may be permitted. People who hide their relativism behind the screen of objective morality could be very common indeed.
If there is no God and believers say there is - and that he is the reason morality is real then they are relativists without knowing it. Then they are the ones who are inventing their relativist morality!
A God who is relativist would be a worse nightmare than people being relativist! Relativists do force their rules on people but if they thought a God was relativist they would be worse. After all you cannot defeat God!!
The other question is how relativist is God? Relativists are usually inconsistent. But God might not be. God may be either 100% relativist or 100% non-relativist. So the worst relativism is that which says there is a relativist God! Religion can do nothing to show God is not a relativist being. It grants no clarity and is part of the trouble.