I believe there is general principle underpinning morality of wanting to act in the best interests of ourselves and those within our moral circle. There is an element of objective morality since, by a large, most people will agree on core fundamental issues but he issue of relativism arises when it comes to the details. For example most of us accept that it's wrong to abuse children but we can't always agree what constitutes abuse and argue over issues such as corporal punishment in schools. Alternatively we accept that killing is generally wrong but when someone does something terrible many people advocate the death sentence for that individual.
One of the core problems in the world is that individuals moral circles are often defined along lines of cultural identify, social standing, religion, race, sexuality and politics to name a few. The perpetrators of crimes often don't consider their actions to be immoral because they don't consider their victims to be worthy of moral consideration. There are exceptions to this such as cases where the person is suffering from mental illnesses or is under strong social pressure to take part in the crime, especially where with the possibility of being subject to violence themselves if they don't take part.
I generally think that most people are decent within the context of their lives.