No user input without checking on every update?

you can do this in many ways and they mostly depend on the way you implemented the game.

one way is to have some boolean or anything else that indicate that your in a cutscene and add to your input conditions

     if(...&&!CutScenePlaying)
     {
     ...
     }

or you can remove/disable the scripts that are used for input in the beginning of a cutscene and then add/enable them at the end

it all depends on your implementation..