I’m sure they care more than that. Global opinion matters, especially if it can influence policy makers, particularly citizens in the western developed countries.
That's only partially true, in a world so communicated a lot of people are going to contact their friends living in Saudi Arabia and tell them what they think about the film, a lot will see this news on reddit or elsewhere and realize its being censored.
Mozilla's death will be one of the saddest dead-horse-beatings to be ever seen. Personally I've switched to Chrome after so many years of using Firefox and I'm not looking back. I'll be stabbed in the back, but I won't say I didn't expect it! Also the knife in my back will be placed by competent people, keeping my bleeding to a minimum ^_^
I've switched because chrome manages my accounts seamlessly across my Android phone and Desktop. It's an unfair advantage Google has. I don't know how Mozilla can compete in the long run.
From your answer, I assume you own an Android phone. Mozilla could compete because Firefox has Sync, but Firefox on Android is some seriously laggy shit with built-in ads, so it's going to be hard for them to win.