It's really not that big a deal. On most islands they are clearly marked with a red band. Don't touch them, don't eat strange fruit off the ground, and don't stand under them in the rain and you'll be fine. Even if not marked, just don't go groping trees. Don't worry about breathing the air, that part is sensationalist bullshit.
What's more dangerous, as tour guides will be happy to tell you, are coconut palms: Falling coconuts are responsible for more deaths per year than shark attacks. (Although that says more about the rarity of shark attacks, I guess...)
Oh well, atlasobscura seems to need the clicks.