Depends on your definition of opt-in. The app has to 'sign up' with the push notification service of the plattform to receive push notifications. But most apps do this by default. I guess that in most cases this makes sense. most people who install an instant messaging app want to be notified of new messages.

iOS push notifications require permissions, but I believe that apps can schedule "local notifications" without requiring permission.

eg: A timer app can schedule a notification at a specific time in the future.

I don't believe push notifications are opt-in, but the vast majority of apps that support it also have a signup / login step to link your phone up with the server doing the pushing.

I'm certain that on both iOS and Android, notifications are turned on by default, and have to be explicitly disabled. Both devices support "Do Not Disturb" modes or similar, which can silence notifications, but to my knowledge they still collect in the drawers by default. I'm very familiar with Android's interface to silence all notifications from an app, as I usually don't care for them. (Twitter's in particular are obnoxious.)