So I have this app that I made before the Android M came out, the app has
Write & Read
Yes, it is possible. But that can give you a big problem. If the user deactivates some permission your app simple crushes because the permission is no longer available. The OS ask the user "This app was developed for a previous android version. disabling this permission can cause unexpected closing of the app" (ore some thing similar). In conclusion this is the normal behaviour because the android version that you are using to compile your app is before permissions needed to be confirmed by the user.
this link explains all you need to now about your question .