Quite funny that you begin by talking about projection and then write this.
How many of the people in Gaza have you spoken to? How much time have you spent, for example, watching the broadcasts of Gazan civilians on social media documenting their daily experiences? It is painfully obvious as I read this that the answer is “almost none” or “none.”
Yet you confidently talk about them as if they’re all “radical Islamists.”
You do not need to go to a "Hamas-run school" to hate the people who have kept you in what is effectively a prison for your entire life. I will never understand why people who I know don't have brain damage can't see this obvious point.
If that kid in the basement grew up to hate and even kill the people of Omelas, would you put that down to some kind of education system? Would you assume that somebody had been sneaking into the basement when nobody was looking and telling him or her to hate?
Or would you think, just maybe, it had something to do with the appalling conditions they kept him or her in for their entire life??????
Sure, religious extremism is a problem. And Islam does seem more susceptible to it than other religions. But it's very hard to radicalise people who are free and happy and have something to lose. Maybe try giving the people in Gaza that before assuming they're all crazed genocidal monsters, eh?