Not a good idea. The Middle East has had a succession of "enlightened" despots who attempted to rid their countries of Islam. Islam is not just a faith for these people, it's a way of life, so well entrenched in the social fabric that all these rulers managed to do was to inflict even worse human rights violations and galvanize the population against the demon West.
You have to let them find their own way. It may take them a few hundred years, but eventually their society will slowly pry open. The external threats to their way of life will have to cease, as long as they feel like they're under attack by the West, they'll just cocoon off and just not allow any influences in.
Probably the best thing that could happen in this regard is a permanent collapse in oil prices, though that would likely cause a lot of people to starve. Things would get a lot worse for them before they get better. I read an article recently about how the Saud family is trying their hardest to prepare for a post-oil world.
> Is there a simple explanation for why the Christian West moved to relative secularism a couple centuries ago while Saudi Arabia has remained so medieval, despite oil-powered industrialisation?
Because colonialism. Europe brought industry to the rest of the world at the point of a gun. An excellent book to read on this topic is Fields of Blood by Karen Armstrong.
The first chapter gives a very good rationale for where hatred and subjugation of the 'other' comes from and the book traces how this kind of socialized violence evolved over the ages.
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