One of the most hidden and less known under the hood upgrades Apple did to El Capitan was a brand new System Integrity Security System (alot of system in there), or rather known to the El Capitan community as Rootless. Rootless was developed to increase security over your Mac's system files, meaning your system will lock you out of important apps and files for the OS, files that the system needs to even boot. The main aim for this system is to prevent any accidental or intentional tempering or removal of system files and to prevent viruses from bricking your Mac.
There is a way to disable it and don't worry, this process will not brick your Mac or ruin anything.
Disclaimer: I will not stand responsible if anything were to happen with your Mac while doing this process. If you wish to do this, it's your own choice. I'm not saying anything will happen, but just in case of the worst possible scenario.
1. Turn off your Mac completely.
2. Hit the power-button and before you can see the Apple logo, hold CMD + R. When the Apple logo appears, you can release the keys.
3. This will boot your Mac into Recovery Mode.
4. On the menubar in the Recovery Mode, click on Utilities then Terminal.
5. Type in the following command: csrutil disable
6. Restart your Mac by pressing the Apple icon on the menubar.
7. Now you should be able to change any icon that may not have been possible for you before.
How to enable Rootless:
Follow the same steps until step 5 and type instead: csrutil enable.
Then restart your Mac.
I do advise you to disable rootless, change the app icon you want to change and enable Rootless again in case you ever come accross a virus or make a mistake by deleting a system file in the future.