Flow of the Game
Far Cry is little different than most open world games. Usually the model is that you have many missions to choose from, some story missions and some side missions. Story missions advance the plot, opening up new side missions, but also closing off others.
In Far Cry 5, almost everything you do- freeing outposts, running side or story missions, killing key hostiles, etc, adds to your Resistance Points. When you hit certain levels of Resistance, the area boss will kidnap you, and you'll play through a core story mission. You can lose access to some missions this way (Fall's End is the primary and most common example), but these missions are marked as 'completed' in terms of story progress- you can still 100% the game even if you didn't actually perform them. If you do want to do everything yourself, consider holding off on the more gratuitous Resistance building activities (ie destroying targets of opportunity) and focusing on the story missions and side missions which interest you. You never lose access to Prepper Stashes, gear, or challenges.
After the end of the game, you can still wander out and complete remaining side and story missions, but enemy forces will be greatly decreased, and all checkpoints will be manned by friendlies. This means that challenges or missions which call for maximum carnage can be harder to achieve.
There is no New Game Plus mode- the only thing that carries over from previous playthroughs are silver bars, and silver-bar bought gear.