Christian and political conservatives don’t feel the need to depict moral relativism in a manner that would satisfy academics or philosophers. The phrase “moral relativism” describes what they believe to be the refusal of society to recognize clearly defined moral guidelines. That secular academics have a more narrow definition is irrelevant. Their depiction is correct, your objections are quibbling over definitions. The wisdom of humans can never trump the word of God.
Being raised a Baptist Preacher’s Kid I can attest that the New Right frequently lumps aesthetic and moral judgments into a single ethical frame. It’s a failure to grasp their own religious teaching in which believers are directed to turn the microscope inward and judge their own behavior, but instead follow the model of the religious and political leaders he most reviled: those who hold others to moral standards rather than themselves.
The Apostle Paul had a different take on moral relativism. To him there was no difference between gossip and murder, both are shortcomings of moral character and it is impossible to attain moral perfection. The presence of grace freed believers from adherence to impossible standards, allowing them to follow a course of morality written in their hearts. He advocated moral judgment against others only in extreme examples.
When Christian conservatives rail against moral relativism they demonstrate a fundamental misunderstanding not only of moral relativism, but their own scriptures.