Same here, Brian. Yes, there's trichlor in it. But I sure don't think you're any more exposed to it than exposure to the nasty garbage in gasoline while filling up your car.
Everyone is different on resistance to chemicals. If the fumes are a significant bother while cleaning, switch to something else. Otherwise, the very small amount needed in the first place shouldn't be a concern.
Now, if you're bathing yourself in the stuff, that's a different story....