Two things come to mind: A different ending to the Great War and a unified Arabia under the Hashemites.
Maybe the US never gets involved in the Great War, but kinda have it to where both sides pretty much call it a draw or something. If someone needs to win, have it be the Central Powers.
A unified Arabia under the Hashemites would have a change to grow at their own pace and without the threat of communism from a lack of USSR or such, it can probably try and do so. Hashemites and whomever Allies they get will crush the Saudis and any prominent Wahhabist.
Beyond that, have them grow and change, reaping the benefits of oil and modernizing at a similar pace to the other prominent nations of global politics. Have the monarchy invest in infrastructure and so on.
The Muslim world’s reactionary stance is, as said, a reaction to the “liberal West.” After all, conservatism and its radical counterparts are based on law, order and tradition (especially religion) from an ideology stand point.
Arabia will likely liberalize at a similar pace to the rest of the world with the end of the Great War and reaping economic benefits. Additionally, should they take on a caliph role, they can fund more liberal schools of thoughts across the Muslim world and so on.