I'd react by looking for super cool hobbies to tempt my child with, like the 3D printing makers' movement, linking them into survival prepping for as long as necessary until his or her focus shifted.
I'm an Aspie who grew up with an Aspie Cold War prepper/survivalist dad and was a prepper right along with him.
My dad became obsessed with prepping after my eldest brother passed away. There was nothing he could have done to protect his son any better, but, by damn he was going to protect his remaining loved ones to within an inch of their lives!
I guess my point is that my dad, though prone to latching onto all sorts of hobbies, latched onto prepping in response to anxiety and fear of further loss. Perhaps you could try to find out what underlying anxiety has begun to manifest itself in this way and try to work on that with your child?
Looking back on our joint prepping activities, they weren't very healthy. It did give us something to do rather than just letting our minds seethe with anxiety but the concepts we were dealing with bred further anxiety. Aspies are planners, but there are much healthier things to plan for than the death or long-term disruption of human civilization.
Skills learned through growing up a survivalist did save my life when I was homeless, but I'd likely have never been homeless in the first place if my parents had focused for preparing me for life in the real world rather than for surviving the world of my dad's nightmares. As an adult, I permanently set my doomsday prepping urges aside because I came to the realization that I had no desire to survive a nuclear war or the complete collapse of civilization. All my favorite things in life are parts of the society I live in or require it to exist.
I think it was my parents running away and my homelessness that brought that into focus. I realized that knowing homelessness could be ended and that there was a society if only I could find a way back into it were the only reasons I tried so hard to survive it. A post apocalyptic world would be far worse, far more miserable, and it would go on for as long as I survived with no hope of anything better.
That may sound horribly depressing from the outside but it was such a relief to reach that conclusion. I could just get on with living in what the world is now and focus my intensity and problem-solving skills on it and on other things like personal development, art, science, writing, and love.