The tanins in the redwood, the microorganisms that keep it from rotting for so long, are not good for breathing. Even when sealed or painted you can still smell that redwood tang.
Of course, sealants have come a long way in the last few years and may now be good enough to completely mask these.
I never really gave that one a whole lot of consideration. I know though that when I was doing custom cages I never had a single request, not did I make on spec, a single cage of redwood.
Made a few decks, but no cages.
That may just bear some further inquiry.