"Can you actually provide this evidence to us?"
I could, but it's 7:57am here, and I need some sleep. And half the information you want is in Arabic, and the other half requires you to understand genetics. And I don't think you actually care about the answer. But you could probably Google it yourself if you could suppress your biases and your snark.
Remember, you're looking for these facts, but not necessarily with the exact wording: 1. They saw the USA as somewhere where people are allowed to do whatever they want far more than in other countries or at least than their country. 2. They strongly dislike that fact or think Americans should have to follow harsh laws about many aspects of their life. 3. They are genetically different from us. 4. Genetic differences are caused by mutations in general. 5. They have personality differences from us that seem to be heritable and lead to a desire for external rules and/or violence.
"Citation needed: I've never seen the people who hate America call it "a beacon of freedom". They tend to call it stuff like "imperialist aggressor" instead. And likewise "imperialist aggressor" is rarely used as a descriptor of America by people who love it.
Firstly, people like Michael Moore call America an imperialist aggressor all the time (because it is), but still love America. "Imperialist Aggressor" is our term. Muslim terrorists don't talk like that as much as we do, because they are also trying to establish an Islamic empire through violent aggression.
Obviously, they are going to use synonyms for "beacon of freedom" rather than saying it word for word. And they would say it in Arabic rather than English, so you'd have no idea what they were saying. They would use an exact synonym like "cesspool of depraved anarchy that's sucking other countries in to their depravity" which means the same thing. What they would never say that the USA is a tyrannical totalitarian dictatorship.
The people you are thinking of, like "we need more gun control" or "gay people shouldn't be able to marry" are a bit hostile to freedom, but still very different from Muslim fanatics who think we need to all pray 5 times a day, cover ourselves from head to toe, never criticise our leaders, and a thousand other laws.
First of all, you're still not showing how it's genetic differences produce these different outcomes. Some very liberal people I know or have read tend to be atheists that were nonetheless born in Arab backgrounds. Nothing you've said, even if I were to concede an actual difference in values, indicates how these different values is produced by genetics rather than religion. Have you seen an Arab atheist argue that we should "pray 5 times a day" for example or "cover ourselves from head to toe"? Probably not.
So is there any correlation ...
We see far too direct a correspondence between others’ actions and their inherent dispositions. We see unusual dispositions that exactly match the unusual behavior, rather than asking after real situations or imagined situations that could explain the behavior. We hypothesize mutants.
When someone actually offends us—commits an action of which we (rightly or wrongly) disapprove—then, I observe, the correspondence bias redoubles. There seems to be a very strong tendency to blame evil deeds on the Enemy’s mutant, evil disposition. Not as a moral point, but as a strict question of prior probability, we should ask what the Enemy might believe about their situation that would reduce the seeming bizarrity of their behavior. This would allow us to hypothesize a less exceptional disposition, and thereby shoulder a lesser burden of improbability.
On September 11th, 2001, nineteen Muslim males hijacked four jet airliners in a deliberately suicidal effort to hurt the United States of America. Now why do you suppose they might have done that? Because they saw the USA as a beacon of freedom to the world, but were born with a mutant disposition that made them hate freedom?
Realistically, most people don’t construct their life stories with themselves as the villains. Everyone is the hero of their own story. The Enemy’s story, as seen by the Enemy, is not going to make the Enemy look bad. If you try to construe motivations that would make the Enemy look bad, you’ll end up flat wrong about what actually goes on in the Enemy’s mind.
But politics is the mind-killer. Debate is war; arguments are soldiers. If the Enemy did have an evil disposition, that would be an argument in favor of your side. And any argument that favors your side must be supported, no matter how silly—otherwise you’re letting up the pressure somewhere on the battlefront. Everyone strives to outshine their neighbor in patriotic denunciation, and no one dares to contradict. Soon the Enemy has horns, bat wings, flaming breath, and fangs that drip corrosive venom. If you deny any aspect of this on merely factual grounds, you are arguing the Enemy’s side; you are a traitor. Very few people will understand that you aren’t defending the Enemy, just defending the truth.
If it took a mutant to do monstrous things, the history of the human species would look very different. Mutants would be rare.
Or maybe the fear is that understanding will lead to forgiveness. It’s easier to shoot down evil mutants. It is a more inspiring battle cry to scream, “Die, vicious scum!” instead of “Die, people who could have been just like me but grew up in a different environment!” You might feel guilty killing people who weren’t pure darkness.
This looks to me like the deep-seated yearning for a one-sided policy debate in which the best policy has no drawbacks. If an army is crossing the border or a lunatic is coming at you with a knife, the policy alternatives are (a) defend yourself or (b) lie down and die. If you defend yourself, you may have to kill. If you kill someone who could, in another world, have been your friend, that is a tragedy. And it is a tragedy. The other option, lying down and dying, is also a tragedy. Why must there be a non-tragic option? Who says that the best policy available must have no downside? If someone has to die, it may as well be the initiator of force, to discourage future violence and thereby minimize the total sum of death.
If the Enemy has an average disposition, and is acting from beliefs about their situation that would make violence a typically human response, then that doesn’t mean their beliefs are factually accurate. It doesn’t mean they’re justified. It means you’ll have to shoot down someone who is the hero of their own story, and in their novel the protagonist will die on page 80. That is a tragedy, but it is better than the alternative tragedy. It is the choice that every police officer makes, every day, to keep our neat little worlds from dissolving into chaos.
When you accurately estimate the Enemy’s psychology—when you know what is really in the Enemy’s mind—that knowledge won’t feel like landing a delicious punch on the opposing side. It won’t give you a warm feeling of righteous indignation. It won’t make you feel good about yourself. If your estimate makes you feel unbearably sad, you may be seeing the world as it really is. More rarely, an accurate estimate may send shivers of serious horror down your spine, as when dealing with true psychopaths, or neurologically intact people with beliefs that have utterly destroyed their sanity (Scientologists or Jesus Campers).
So let’s come right out and say it—the 9/11 hijackers weren’t evil mutants. They did not hate freedom. They, too, were the heroes of their own stories, and they died for what they believed was right—truth, justice, and the Islamic way. If the hijackers saw themselves that way, it doesn’t mean their beliefs were true. If the hijackers saw themselves that way, it doesn’t mean that we have to agree that what they did was justified. If the hijackers saw themselves that way, it doesn’t mean that the passengers of United Flight 93 should have stood aside and let it happen. It does mean that in another world, if they had been raised in a different environment, those hijackers might have been police officers. And that is indeed a tragedy. Welcome to Earth.