It is very hard to say in any objective way how American society changed after the attacks. In order to have an objective summary of the changes, we would have to have done extensive research on things like opinions towards Muslims and towards government security programs on September 10, 2001. We would then have had to carry out that research again at some point after the attacks. Thus, we cannot objectively determine how American society changed.
However, this is a problem that often faces historians. That means that we have to do our best to ascertain how things changed. We can try to do our best to think about what seems different since 9/11. I would argue that there are two main changes that can be seen.
First, our society seems to be somewhat less tolerant, particularly of Islam. Since the attacks, more Americans have come to feel that Islam and Muslims are inherently anti-American. This is not to say that all Americans feel that way. However, we can, perhaps, see this sort of attitude in the pervasive allegations that President Obama is Muslim.
Second, our society seems to be more willing to accept intrusions on people’s rights in the name of anti-terrorism. We are generally willing to accept that other people will be tortured if they might be terrorists. We are willing to accept things like the Patriot Act and the NSA surveillance programs that have recently come to light. We are willing to accept the hassles imposed on us every time we try to fly.
I would argue that these are the two main impacts of 9/11 on our society.