This is governed by the user setting 
only_send_chat_push_notifications, found in /my/preferences/chat:
There is no site setting to control default behaviour.
First, this is quite buried and might be better to also live in /my/preferences/notifications, which is where I would naturally look. Also, I wish that I could set this to be default TRUE for my instance, so that my users ONLY get chat notifications on their devices (unless they want more).
The key problem is that the majority of Discourse notifications are not urgent; their asynchronous nature is one of the strongest reasons that I 
Discourse! Having them as push notifications is just irritating, as I get way too many, and they just don’t deserve to break my attention. They can wait until I visit the site (or read the summary).
Chat, however, is firmly ephemoral and much more synchronous. Thus, it makes sense to me to allow chat to have the push notifications, and suppress them for everything else. I can do that easliy enough for myself, but it is jolly hard to set the default behaviour and/or make it easy for my less savvy users to do so too.
Workaround
I can work around this (I think) by using a custom Update Profile action of the Custom Wizard Plugin 🧙 on a joining wizard (must work out how to do that!).