Hi, try this method, it works for me on an iphone4 & 4S (iOS7)
make sure you have all apps closed before next steps.
-Go to Settings, Phone, Show My Caller ID. (if button is Greyed Out)
-Pull down Control Centre & Turn On Airplane Mode & return to Show My Caller ID screen.
-Now slide your screen from right to left taking you to another screen, then slide back to your Show My Caller ID screen.
-Now You Can turn ON or OFF your Caller ID Button.
-Lastly slide down you Control Centre again and Turn OFF your Airplane Mode.
Thats it Job done.
Please note, it will now stay in the mode that you have chosen(ON or OFF) even if you respring or reboot your phone. But if you return back to
Show My Caller ID screen, then you SIM Provider will automatically Disable your Caller ID screen BUTTON once again. So just repeat the steps
above and your be fine.
Hope this helps.
🙂