Selective switching off
To turn off the push messages of certain people, you have to click on the icon here. This way you can selectively choose who you want to get pushes from.
With this setting you choose whether you want to get push from the user or not. Either you get all push messages or none at all.
That’s the push messages we send at the moment.
To disable messages in general you have to go to the system settings of your phone: