Some people who drop their belief in god also drop the idea that there is objective truth in morality (aka moral realism).
Why do they do that? It’s because they believe that moral realism implies demanding obedience to one’s moral views. They treat moral realism and demanding obedience to one’s moral views as a package deal - as if you can’t have one without the other. And since they are against the idea that people should demand obedience to their moral views, they reject the whole package, instead of just rejecting the one idea they have an actual problem with.
The thing is, the best knowledge we have to date about the truth regarding morality is that it is wrong to demand obedience to one's moral views.