There is nothing contradictory between rightwing and leader of muslim world if you look closely. The scale of bombing that Russia did on Syria is not comparable to what Israel managed in Palestine and the people holed up in Idlib and Turkey are most probably in worse condition.I doubt Saudis will normalize relations with Israel anytime soon. They view themselves as leaders of the Muslim world so they need to pretend they sympathize with Palestianians and support their struggle for statehood. Normalization at a time when Israel has the most right-wing government in its history (with actual ziofascists holding ministerial positions) would simply be a poor look for them.
Saudis look at hundreds years of history and see who got promoted during ottomans and there backers in Europa. Saudis also deep understanding of technology as they have that longest continuous relationships. so if some one get retire and comes on board of firms. they still visit Saudi. I mean Japan had been selling high end Toyotas to them since 1950s so they know what to expect and what price range. if Japanese long term quality declines than we will know from them.
They are not going to change there western health system or Intel business laptops and certainly not Western Aviation that so much depend. I mean they literally custom orders Civil Aviation jets that are way overpriced than regular commercial jets.
since there country is so large relative to population with so many countries surrounding them and inside large immigrant population they also put premium on intelligence. so they need multiple sources of intelligence to make sure the information is correct. Israel can be one of it.
who knows what Israel produce domestically as they may not need to export the best custom chips.