I'd distinguish between prepping and doomsday types. Prepping can be as simple as having some basic supplies and nonperishable goods such that you're not going to die if, for any reason, you need to survive independently for some period of time. It's not like some lifestyle or even dependent upon an assumption that you'll even ever need these things. So it's a relatively low cost decision to be able to be at least somewhat prepared for an eventuality that, though extremely improbable, would have disproportionately negative consequences if you were of the 'do nothing' extreme on the other end.

To put it mathematically, if I said there was a 1 in a million chance of you losing a billion dollars sometime in your life, and you agreed with me, it'd certainly be logical, if you could, to provide insurance against that eventuality for $1. In fact it'd still be mathematically sound to spend $1000. But this is for an event that you are literally 99.9999% sure will not happen. I think the big difference is in seeing reality as a neverending stream of probabilities as opposed to seeing reality as a neverending stream of certainties. The probabilistic mindset can lead you to conclusions and decisions that look peculiar to a deterministic mindset. By contrast doomsday types are those who have a deterministic mindset and have decided that the world (as we know it) is going to end and thus make that a part of their persona and worldview. Granted, they could also be of a probabilistic mindset with a different weighting but, at least in my experience, that's not usually the case.