Do objective morals exist?
This is one of my favorite questions to answer. I tend to be skeptical of objective moral theories because they tend to not have good grounds for its ontology and epistemology.
When it comes to ontology, I question how objective morals would exist in the Universe. If the purpose of these morality is to preserve order and survival, then I would think morality needs to be consistent for all of existence. But what we have now are different things (humans, viruses, artificial intelligence, etc.) with different moral codes all interacting in the Universe, which leads to the question of who or what is supposed to survive and what decides that. We don't know that humans are meant to survive given the fact that there's so much natural evil in the world. We can follow the rules perfectly and suddenly get hit with a huge asteroid or some pandemic that wipes us out.
When it comes to epistemology, I question if we can reliably know what morals are objective vs. subjective (based on culture and opinion). I would think that there would have to be some objective or scientific way to discover such rules, but as it stands we don't have that. Some say that we can have a general consensus on some of the basic things like do not murder. I question even that because of what I've seen that politics can do to people, leading us to disagree on even the most minor of things. I've seen people argue over if such things are allowed when race is injected into the mix, and in other cases I've even encountered people (mostly Hamas supporters) justifying the murder of children and women.
Basically, I think what we have is just faith in objective morals. Despite all of this, I don't live life in some amoral way, but rather I try to form moral opinions based on what most or all sides could agree with. And of course, to keep myself from facing legal consequences, I follow the law. So rewards and punishment does help either way, as most want rewards and little to none want to be locked up in a cage. Just my two cents!