Something like this:
New setting called "*deny". When you can't read a card, you look for its *deny rule and render that instead.
If you're rendering a :read view, then you render the deny card in the current view. If you're in an edit view, you render, what...content?
Note that you could have a chain of *deny views. Eg, there's a card called Super Secret of type Clandestine and a card called Kinda Secret of type HushHush, and you have these rules:
this basically works with the denial view. My inclination is now not to create a setting but rather to work on making views overrideable.
add setting - what you see if no permission to view+discussed in support tickets
add setting - what you see if no permission to view+relevant user stories