This is an older question but still appears at the top of a google search so I will update with information from 2023.

Apple introduced support for Web Push in webkit iOS and iPadOS 16.4 (2023) https://webkit.org/blog/13878/web-push-for-web-apps-on-ios-and-ipados/

This change means that apps such as PWA (Progressive Web Apps) or side loaded apps can also receive push notifications. https://developer.mozilla.org/en-US/docs/Web/Progressive_web_apps Progressive Web Apps are apps built in Html/JS which can run cross platform without different code bases.

Push notifications use a IETF open standard which can be used for both iOS and Android devices.
https://web.dev/articles/push-notifications-how-push-works

This cumulates to mean that its not longer required to have an apple account to create apps for iOS AND for these apps to receive push notifications.