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.
Others have given good reasons, but many people join very strict religious orders in other religions. And some of those have been very militant.
It's easy to get people to hate The West, and their own governments, and the increasing alienation of their lives as capitalism elides all cultural social bonds. That's the same thing that leads to what Marx called "reactionary socialism", the urge to retvrn to a rural ideal that is no longer materially possible.
It's also easy to get people to accept an ascetic religious life. Regular rituals, fellowship of others and discussion, a simple life, without the distractions and mistakes and disappointments of real life. Its just the more systemised version of the urge to go live in a yurt in Mongolia after a bad breakup or when you've fucked up particularly hard.
Combine them. Have the material fire of reactionary/agrarian social tendencies, and feed it with the superstructure of monastic mysticism, but without the disengagement with the world. And you have a radical.
All the book burning and misogyny is (mostly) either bolt-ons or hold outs of the collapsed reactionary ideology