Funny since it's widely sold and used as a household cleaning agent eh? Makes you wonder what manufacturers expect you to do - move the toilet outside the house before cleaning it, perhaps. Sounds like more of a chore than it usually is.
Don't mix household bleach with acids as chlorine gas will be formed. Other than that, it's not a huge concern really.
Bleach is pretty effective in dissolving fat/grease, hence the recommendation for gloves. Not everybody likes dry skin.