The guidelines specify that I “should provide an image that has 90° corners (it’s important to avoid cropping the corners of your icon—iOS does that for you when it applies the corner-rounding mask)”
I see lots of apps that disobey this recommendation. How big is the risk that Apple will reject my app based on the app icon’s rounded corners?

I’ve done this before and haven’t been rejected for it. Just make sure that your icons corners align properly with the corners applied by iOS. (could look pretty strange if they didn’t) As long as the fact that you’re manually setting the corners isn’t obvious to the user you should be fine.