Mac App Store keeps prompting me to upgrade iTunes
Are you certain that you in fact have iTunes 12.5.1 installed?

Have you manually checked the version?

Seriously, this may be a gift from heaven, if it is your phone. (Tagged as iOS and screenshot is MacOS so I will address both)

The problem is happening on mobile devices and Macs. 

The MacOS fix is to manually download iTunes 12.5.1 package and install it that way. 

If the link above to Apple's iTunes Download page does not load for you, here is the direct link to Apple's main iTunes page. 

For iOS, there seems to be a big problem with people reporting bricked phones.

Go to systems-->notification find the app you do not want to see notifications from and choose "None" as the alert style. Or you can completely kick any app from the notification center.

You can disable most unwanted pop-ups by setting Software Update/ App Store to not automatically check for updates.