I would say an objective morality is one that considers the well-being of humanity its highest priority. Before you point to Marxism as an example, I’ll point out that their naïve belief in forcing financial equality is NOT in the best interest of humanity, and that believing in God wasn’t enough to invest the Muslim world with a morality we can really rejoice in.
The Muslim god is not our God.
You can have subjective morality, but it doesn’t have the same meaning as objective morality. And it’s not really a valid system of morality.