Interesting question! It's actually more complicated than it sounds, but also because of incorrect information displayed in the Bestiary. Before going into our (mines and Hunter of Dragoes') discoveries, let me mention that in TibiaWiki's bestiary simulator all creatures are currently shown with the swords icon. That tool currently does not support this icons data, and that is just a static image for all creatures (something we plan on updating).
The first thing we verified is that No Harmless creatures attack you, even when challenged or summoned. In fact, all Harmless creatures have the "Creature does not attack" icon in their bestiary:
Moving on to Trivial creatures, you have noticed that some such as Sheep won't attack you even though they have the swords icon. That's a mistake in the bestiary. Creatures like Sheep also have "Skill = 0" in their configuration file (this can be verified through the leaked server files). The reason these creatures are not categorized as "Harmless" in the bestiary is that they drop loot. In order for a creature to be Harmless, it must not attack and must not drop any loot. And as it turns out, it looks like Cip decided to use the Icon only on Harmless creatures, instead of using it on all creatures with Skill 0, which should also display that same icon. This will be reported to CipSoft after I finish writing this answer.
With that explained, we can now start building our list. We can start by skipping all Harmless creatures. When looking at Trivial Creatures, we have:
- Adventurer
- Bog Frog
- Deer
- Flamingo
- Green Frog
- Horse (all 3 colors)
- Parrot
- Seagull
Pigs and Butterflies are special cases. Even though they will attack when challenged or summoned they cannot kill anything because their Attack value is 0 (even though they have FistSkill > 0 which allows them to attack). All their hits will "poof" because of that.
Surprisingly, there's actually also one easy creature that will not attack you: Calamarys.
There are probably other creatures as well that are only summoned by other creatures or from events, which will be a little harder to test.