what you ask is actually a trick question.
but I believe I can give you an answer you are looking for. please follow till the end. I will do my best to answer your question first, then I will give my personal opinion which I hope you find useful.
Truths cannot be denied and are absolute. As I mentioned earlier examples, here's another to clarify the point. To be typing this as a human, we need a beating heart. Without a beating heart you or I cannot be typing this. Just a lifeless piece of meat. 100% infallible. You can check for yourself right now how many bpm.
Morality by it's very nature is derived from a few elements by their very nature are not absolutes but relatives. The major elements involve life itself, emotions and social relations. Per life itself : When you kill a chicken to eat it, you are valuing your life above the chicken's. How can you absolutely value one life over another? Well you devalue the chicken's life, so your morality now makes it acceptable for you to kill a chicken for chicken rice, KFC or for kari ayam. Tastes delicious but costs a life. Because the reward to us is so tasty and so filling, we make that unconscious choice that the chicken's life is of no consequence. But suppose for a minute that the chicken was larger than us and found us tasty. What then? The chicken would eat us. We would now be really upset now that the tables are turned. So in the first case, most people find it moral to eat a chicken, but allowing a chicken to eat one of us would be unthinkable. How do you get an absolute truth out of this other than for the conclusion that it's all about who has more power and nothing to do with morality?
I don't want to type too much so I'm compressing this example. Per emotions and social relations: You and your child love playing in this stream. After a long time doing so, you learn that someone has come along and bought the land and demanded that you stop doing so and never trespass again. How to give an absolute answer for morality in this case? The land was available for sale. You never bought it and just enjoyed it because the previous owner chose not to bar you from it. It was a lucky privilege. If you demand the right to use that stream, you are denying the guy his right to enjoy his stream in peace bought with who knows how much blood, sweat and tears. If you chose to spend all your time playing in the stream instead of working to own the land it's in how can you now determine who's right? You for your pure joy in this stream or the other guy who worked to own it? And for all you know or don't know, he's enjoying it even more or even less than you.
So short conclusion is that morality is determined based on lots of factors that are not absolute. To use the previous example, if every family had 30 streams to play in, no problem. But what happens when 30 families have 1 to play in? This is when morality comes into play. And because different parts of the world had different environments and different pressures, moralities
WILL differ.
I give you an easy example. Moralities between the Chinese and Malays will always differ. Why? Because they come from 2 different environments. One is historically a plain-dwelling farmer and the other is historically a jungle-dwelling hunter-gatherer. Because of the surplus food production of the Chinese, they had time and resources to grow a massive population, technology and social structure where competing against one another was the prime mode of operation. Whereas the Malays with less food and resource surpluses stuck to their lower level of population that stressed co-operation instead of competition for survival. Because of this, the two races can never easily understand each other. So who has the more "truthful" morality? They both are. To their environments.
Once you have too many people as we have now, all these different impulses and moralities will conflict. Let's not forget to to mention that individual humans vary in emotions. Some feel more, some less, some murderous, some protective and so on.
Given all the noise I've just produced above, I will state that for my personal answer
generally speaking, the greatest crime against morality is killing. A very close second is violence against another person, whether it's physical or sexual. Then you have your property crimes. I believe these to be to the list that's valid.
Now that I've said that, I will give examples that counter my opinion to show you that it is not an absolute. These are "crimes" against reputation. Most people in this part of the world will sue each other to ruin for defamation. I think it's garbage and an excuse for
emptiness and vindictiveness. It should not be against any morality to question another's reputation. You questioned mine earlier, so what? I'm prepared to answer for myself. Another example is that for some parts of the world, physical violence between men is considered normal and theft is worse. For other parts sexual violence against women is nothing compared to theft. These I believe to be wrong.
My basis for this is that what I believe are true crimes are the ones that make people sad, really sad. Whereas everything else that upsets you or angers you is just a primate (monkey) reaction to defending your territory or "rights". Understandable if you're an animal. This is the best I can do to come to an absolute with all these relativities.
So if I have a Bible or a Koran or a Torah, it would read something like this : Don't make people sad for nothing. Make people happy (absence of sadness). To make people happier, you sometimes have to go through and put up with hard times. Other times, just trying to be happy without work involved will lead to sadness. And importantly, don't mistake greed, lust, avarice etc, etc, as happiness, but rather happiness is an absence of sadness-inducing events or conditions. And sometimes, some people just want to make other people sad no matter what. These are your criminals against morality.
This won't be popular because it's too simple and barely even a paragraph, but it is my best answer after all the searching I've done.
Hope you find it of use.