See also How-To Guides.
Push notifications from web sites have long annoyed me—I regularly reset Safari for various reasons (including testing), and some sites pop up alerts demanding my attention as to whether I want push notifications. IMO this kind of obnoxious design is a good reason to de-bookmark a web site.
At long last I figured out how to configure Safari to block all push notifications permanently. Or rather, to never ask me about them. Somehow I had missed it before due to its ill-considered UI design, being out of sight way down at the bottom.
Uncheck that box at very bottom, and those annoying popup dialogs stop appearing.