Dolphin is in kind of a transitional period right now. For most of the history of the Android version of Dolphin, Dolphin has requested the permission to read and write to all of external storage, and has used it for two things: For putting your settings and save data in a folder called dolphin-emu, and for reading your games. About two years ago, Google started pushing the concept of scoped storage, which means forbidding apps from requesting access to the entire storage. Dolphin will have to be compatible with this policy starting in November 2021 in order to be able to keep publishing updates on the Play Store. Currently the game reading has been fully moved over, but we're waiting until that November deadline with moving over the handling of settings and save data, because not being able to access the full external storage means we have to store this data in a folder which gets deleted when uninstalling the app instead of being able to store it in the dolphin-emu folder (and some people don't want this, though I suppose there might be some people who want it as well).
Now, there being a crash is unintentional. It should probably show you some kind of message instead. But what I can tell you is that if you wait until November this year (or possibly December depending on how our release cycle works out), then you will be able to deny Dolphin this permission, and Dolphin will work fine anyway. In fact, if you do a fresh install of Dolphin on Android 11 and newer, Android won't even let you give Dolphin access to all of external storage.
Now, there being a crash is unintentional. It should probably show you some kind of message instead. But what I can tell you is that if you wait until November this year (or possibly December depending on how our release cycle works out), then you will be able to deny Dolphin this permission, and Dolphin will work fine anyway. In fact, if you do a fresh install of Dolphin on Android 11 and newer, Android won't even let you give Dolphin access to all of external storage.