We will always need to have the 'bad' among us so that the 'good' would know the difference. Getting completely rid of 'bad' is simply not possible. If some form of 'bad' is completely eradicated, new forms of 'bad' will replace it. Without something being classed as 'bad', nothing could really, in the end, be 'good' either. As humans we desperately need to know what is good.
All in all, 'good' is a singularly relative term. If there is nothing to compare a possible 'good' with, the whole concept of 'good' would become quite meaningless. Also, if all people would behave exactly alike, there would be no need to classify any of them to 'good' or 'bad'. The utter complexity of human and social behavior is the reason why such ideas need to be created and maintained.
On the other hand, could there be such things as 'good' or 'bad' monkeys? Of course, there are; the ones who do not disrupt the social cohesion are quite certainly seen as more 'good' than those who do by other monkeys. So, the idea of good and bad is not just a human idea, but an evolutionary necessity. Classing different forms of behavior 'good' of 'bad' can greatly help the herd. In the end, this idea can help the whole species to survive and flourish.
However, the modern idea of some kind 'universal morality' is purely a human cultural invention that has been invented and used as an ideological tool mostly by religions. A very basic sense of right of wrong or a rudimentary sense of justice is really inborn in almost all of us.
One must naturally exclude sociopaths and psychopaths, who often seem to have lost this very ability. However, it is a quite different thing than morality.
Normally morality is, in fact, mostly about following the social rules. These rules can be in turn be classed as 'good' or 'bad' according to the results that do produce for individuals and the general flourishing of the society. In fact, following of the current moral rules of the society has also always lead some people into major wrongdoing.
The instinct to follow the current rules of the herd is also an inborn instinct also in humans. We also generally want to please the people whom we respect or on whom we are dependent on. At the same time, we are also guided by an inner sense of justice and fairness.
However, the exact things and actions that are seen as moral or immoral do vary immensely from society to society. They can vary immensely also in the same society at different times and stages of its development. A man who takes part in a stoning of a woman who is suspected for committing adultery needs often to suppress his inner sense of right or wrong. He needs to do this to be able to act according to the currently dominant form of morality in his society.
At this point, I want to stress that commonly agreed form of morality has a very important role in maintaining cohesion in all human societies. Declaring what things are seen as moral and which as immoral makes it clear to everyone what is the desired mode of conduct in a society. Knowing the exact boundaries of allowed behavior does make social life easier.
However, it is pure lunacy to claim that there would be an inborn sense of morality that would say that masturbation or looking at beautiful young women would always be immoral. These things are transmitted purely culturally. Moral inhibitions associated with them are quite unknown in very many cultures.
There simply are many things that will disrupt the social peace in most societies. They are forbidden in almost all societies. The killing of other people without direct orders coming from the leaders of society is forbidden in nearly all societies. It simply is the most disruptive single act an individual can commit in any society.
The forceful taking away or stealing of other peoples property is another thing that is forbidden in almost all societies. It has less meaning in societies where resources are communally owned. The disruption of existing bonds between a man and a woman is also quite universally frowned upon.
However, all these things do stem from the quite universal needs of the human societies. This is the real reason why they seem so universal, not that humans would have some kind of gene for a certain kind of morality. However, we do have an inner sense of justice and fairness. This is the case with mice and rats too according to recent studies. These instincts are necessary for all species that do live in proximity of other members of their own species.
In all modern societies, the needs and demands of the society are codified in some kind of set of universal laws. These laws do not normally follow from any kind of inner inborn morality. They are brought about by the current needs of the society or from the demands of some religions organizations.
However, their overall structure is very often influenced by our species-specific sense of justice, if it is allowed to play a role, which is sadly not always the case. In modern western societies, the needs of the society are more and more based on the needs and best interests of the individuals.
Individuals have also a chance to start to initiate changes in them if they are seen as repressive or outdated, but again any of this does not follow from any kind idea of 'universal morality'.
PS. After saying all this I must also conclude that Immanuel Kant's famous 'Categorical Imperative' may be a valid logical construct in a way that he himself would not ever have foreseen. It may well be valid as an abstract idea. On the other hand it has no bearing on how human morality and human social rules are constructed in practice.