That's not at all what is happening in a crowd crush situation. As explained in the video, above a certain crowd density, people physically lose the ability to control their movement in the mass of bodies and involuntarily behave more like molecules in a fluid and less like individual actors. The people in the back of the crowd, who still have agency in their movement, don't know that they're indirectly causing the death of others, they're not homicidal maniacs (for the most part).
Blaming crowd crushes on the lack of "critical thinking abilities" and "commitment to some ideology" is intuitive, easy, and wrong. A wrong model for a problem will prevent you from finding an effective solution – as seductive as that model may be.
The people in the center of the crowd who die had plenty of opportunities to get out, but they didn't; they committed to their respective ideology.
Sure, if you find yourself in a mass of people that is so dense that you loose any sense of agency, it might help to remember that you're just a molecule in the mass and go with the flow. But if you find yourself in such a situation, it's usually a clear sign that you haven't always been reasonable on the way there.
The people at the interface of that phase change have the choice to move backwards, but still press forwards even though it puts them into physical contact with other people. They can be partially excused for not knowing of the situation ahead of them, but they're still (usually, except in cases of fire/etc) making a free choice to physically touch and press themselves into and against other people. I am talking about people at the interface, not in the middle of it.
If everybody in the crowd refused to voluntarily press somebody else, then no forces would be transmitted through the crowd. But pressing other people, particularly to jostle your way past them, is the nature of crowd psychology. For this reason people should avoid crowds entirely. Being in such a high density crowd is usually a choice.