F4SE not required for updated and modded game.
Ideally, if F4SE would ASK me if I wanted to continue to load the game after telling me it is out of date, instead of just shutting down, problem would be solved.
Out of the 120+ mods I am using only 3 rely on F4SE: Looks Menu, Place Anywhere, and Achievements. I only use the Looks Menu when I'm creating a new character and I can still create new characters without it. There is a replacement mod for Place Anywhere called Place in Red Reborn that doesn't need F4SE as far as I know. And I don't really care enough about achievements to not play the game just because my game is flagged as modded.
To continue to play without F4SE, I go into Nexus Mod Manager, disable the 3 affected mods, run LOOT to reorder my mod load order, and then launch the game directly. Whenever F4SE and the 3 mods that need it get updated, I'll go back to using it.
You can check to see which, if any, of your mods use F4SE by going to steam>steamapps>common>fallout>data>f4se>plugins. If this folder doesn't exist, you don't have any mods that use F4SE and don't need it.