I'm trying to empathise with them... I get why people become radicals of other kinds... but saying no music, no sex, live by the book, behead those who disagree... what part of that makes people think "I want to get into this, this sounds fun"?
The Arab world has valid grievances, which motivated 9-11 for example, but there's more to it than that.
When European, at first Christian and then secular colonial powers run rampant over your culture and people for 100+ years, and demonize your local majority religion as barbaric for almost as long, practicing that religion becomes an act of anti-colonial resistance in and of itself. A way of rejecting outsiders' attempts to define "correct" beliefs and morality on their own terms.
Then there's also the element of practicality. At least in Palestine and Lebanon, a lot of the secular leftist anti-colonial movements have been hollowed out, smothered and/or discredited over the past several decades, leaving more religious groups like Hamas and Hezb Allah as really the only resistance-capable game in town.
Also also, there's a social element to it. Class differences can sometimes feel abstract, and religion, like race or narionality, offers a way to cut through that abstraction. A clear way of differentiating colonized in-group from colonizer out-group.