I had this same problem on my MacBook Air running OS High Sierra 10.13.3 ... here is what I did:
(apple icon at top of screen) > System Preferences > iCloud
This generated a window with a list of apps that can be shacked up with iCloud. At the very top of the list was the nagging notification about two-factor-authentication, with a "continue" button.
Hitting the continue button generated another small window with three options: turn on, learn more, and not now. I clicked the "not now" option, then "continue" button at the bottom of that window.
Voila! Nagging reminders about two-factor authentication and associated annoying red badge on my system preferences icon are all now gone, and I am happy.
You're welcome, everyone