A few days ago, I had this incident where a user repeatedly commented on one of my posts, whilst deleting previous comments (so other users would only see their latest, innocuous-looking comment). My phones (I have an Android phone (personal) and a work iPhone, both with the Stack Exchange app installed) kept buzzing every few minutes. Unlike on SO, mods aren't that active on the smaller sites, and my flag on that didn't get handled until hours later. I muted notifications for the SE apps in the meanwhile.
Now, comment notifications on the sites, I can easily ignore. After all, they do not affect anything outside of the browser tabs in which the sites are open. However, notifications on my phone are a different case altogether. I take them very seriously, and do my best to keep junk notifications to a minimum. That I enable notifications so that users whom I'm helping or who are helping me can communicate more efficiently with me does not mean that I'm also permitting users on the site to harass me with notifications. And notifications that do affect the real world, like on the phone, can become harassment.
The apps should really have a feature to mute a user, or at least mute a post.