Marshmallow introduced the Allow / Deny permissions feature when installing apps. This is a security feature aimed at ensuring you can control what your apps can do and have access to. If you find yourself unable to tap Allow but able to tap Deny then this guide will teach you how to resolve this issue.
The source of the problem is one of your apps which puts an overlay on the screen. In one case I encountered, it was a Sidebar Launcher. In another case, it was a file A manager.
A temporary fix for granting permissions to the App is to go to Settings > Apps > Locate the app > Tap Permissions > Enable the desired permissions > Reboot the phone.
The long term fix is to locate any app you suspect uses an overlay on your screen (Under Settings > Apps) and force stop, freeze or uninstall the app.