I sorted out my problem with the game not recognizing the mods I had enabled in the latest version of NMM. It seems that if there is a mod in your load order that the game doesn't like, it rejects the entire load order and disables all the mods. In my case, the mod the game didn't like was Depth of Field Remover. I narrowed it down to that by disabling all my mods and slowly enabling them and loading the game. With that mod uninstalled, I can now enable my mods in NMM, and load the game and play without messing with the in-game Mods menu.
So, if you are having problems, try disabling them all and then gradually enabling them in small groups to see if the game will load them.