If you're developing apps for Android or iOS, there are exactly two push notification frameworks: Firebase and APN. There are wrappers around it, but they all end up going through the same servers, because polling for notifications drains the battery like crazy; that's why push message sync has basically been reduced to a single, OS managed system, that integrates with power management.

There are alternatives (i.e. unified push) you can use, but they'll require a broker (your app or another one) to be running in the background. Very few people use compatible clients, I'd only expect these protocols to work for either alternative vendors with their own private push message system, of the tiny market of open source enthusiasts.

You can try blocking Apple's and Google's servers and see how they behave. I expect some, if not most, of them to stop receiving timely notifications, and the rest to only receive notifications for a while after they've been used, or prompting you for additional permissions to be exempt from your phone's power saving features.

If you need push notifications on mobile phones, the best you can do is implement some kind of encryption before transmitting the notifications, but to gain any decent chunk of customers, you'll never be free of vendor servers.