So, for the every-pred example, I'd prefer to use clojure piping for better readability:

  (->> people (filter :admin?) (filter :mod?))

This is admittedly a matter of taste, though.

For the some-fn example, I would argue that the usage in OP is a very idealized and tuned example... how often do you really want to say "try this one predicate and if that doesn't work, try this other one"? I only need to do that maybe a couple of times a year (when parsing some sort of irregular raw data) so it's rare enough that I'd prefer to write the predicate explicitly instead of using this sort of succinct predicate composition that could become a "head-scratcher" at a future date.