If God exists, there's still no objective morality
Humans who are not mentally ill. have an innate morality.
Well I wouldn't call it morality, it's more empathy and a natural desire not to see other beings suffering. Morality is more of an arbitrary thing that can mean whatever a given person, religion or culture wants it to.
Exemplified by how humans no longer stone gay people or adulterers to death for example
Not only is doing that an affront to human empathy but it is also irrational, hating gay people or even believing that people should have monogamous relationships is something you are conditioned to believe and not necessarily something people would even consider without being taught to think about it a certain way.