Saudi Arabia was funded by the salafist movement, so it doesn't make sense to speak about a salafi derive. Their funding movement killed tens of thousands of muslims deemed by them as heretical.
Supporting Shari'a law don't have anything to do with prohibiting women to enter in stadium. If you go in same US state and ask "do you think the Bible should be the primary source of law", you will get equivalent number.
Because what muslims understand by "shari'a law" is significantly different from how westerner understand it. For many people, it mean the end of the corruption and justice.
Ottoman Empire was ruled by shari'a law and here it's what an English woman would get from her travel in the 18th century:
“As to women, as many, if not more than men, are to be seen in the streets [i.e. going about their daily activities, etc] […] I think I never saw a country where women may enjoy so much liberty, and free from all reproach, as in Turkey […] The Turks in their conduct towards our sex are an example to all other nations; […] and I repeat it, sir, I think no women have so much liberty, safe from apprehension, as the Turkish – and I think them in their manner of living, capable of being the happiest creatures breathing.”
– Lady Elizabeth Craven, A Journey Through the Crimea to Constantinople, 1789
Source
The issue about apostasy is also very difficult to grasp, even if i don't deny that there are some group which is pushing it. Because it's associated with other ideas that make the ruler as an apostate if he is not applying the shari'a law.
Anyway it could be easily ruled out from a shari'a perspective and many scholars did.