Rabbits jump away when you approach them, and even if you have invisibility effect they still jump away.
Related issues
Comments
00Pokemon00
if you would notice ALL mobs see the player with invisibility effect the effect does not shield the player from mob tracking or them seeing them this might not be an intended feature or it might be intended but this is known and is not a serious bug anyways
What do you mean invisibility doesn't prevent mobs from seeing you? I thought that was what it is for. In fact, I tried it and invisibility does prevent mobs from seeing you (http://minecraft.gamepedia.com/Status_effect , see Invisibility. It does note that some mobs see players regardless, that is not an intended feature.) until you either hit or rub up against them. However, invisibility also does not work with Ocelots, and I believe this is what you meant by saying that this is a known bug. Apparently invisibility only works on hostile mobs.
qmagnet
Perhaps this report should be merged with MC-10901
qmagnet
I guess we could add all this to MC-10901 and make one report about mobs seeing invisible players. Oops... I didn't realize I commented the same thing last time.
Sonicwave
Confirmed in 1.8 (for Ocelots). Rabbits don't seem to run away anymore.
Please don't put down the affected version as a future version, as you don't have access to it yet.