Human anatomy would look different.
We would have slightly different teeth and our mouths would probably be smaller. The big intestine would be shorter and the appendix would probably not exist anymore.
More notably would be the legs. Humans evolved to have strong legs and a big Gluteus Maximus to enable upright running over long distances. This was nesseccary to hunt big herbivores over long distances. Our hairless skin is also an adaptation to running for a long time.
Apart from that, if we never domesticated big herbivores to provide food, we would have bred insects to provide food. The number of domesticated animals might be smaller, but the size of insects bred as food source would be bigger.
The first important civilizations would probably have arisen in places with many naturally occuring insects like the tropics and sub tropics. On the other hand, arctic and sub arctic regions like the north of Canada, Greenland and Scandinavia would be populated very scarcely or not at all.
There's a theory that the origins of civilizations are people gathered around a fire, waiting for the food to cook. Insects don't need to be hunted and shared among the group, so there might be no civilization at all.
Religions and Gods would probably look different, too. Many ancient gods have the faces or bodies of important domesticated animals, most prominently cows. The only insect god I know of is an egyption one.
Our wildlife would be much changed. European sailors released rats (unintentionally), pigs and rabbits (both intentionally) to any island they found to provide food to shipwrecked sailors. These caused the extinction of many endemic species. Some animals like the Dodo and Moa bird went extinct because of the unending hunger of men. Insectivore humans would have introduced insects into foreign islands and continents instead, maybe with less consequences than mammals, maybe with unforseeable ill effects.