Did premodern Europeans and Americans eat bugs?
How far back do you want to go? The ancient Greeks ate insects. Aristotle wrote at length (Historia Animalium) about eating cicadas. He said that they taste best during the late larval phase when they become nymphs, just before the husk breaks. And that in the early stages, male larvae taste better, but after they develop eggs, female larvae are better.
The ancient Romans ate a lot of bugs. Pliny the Elder wrote in Naturalis Historia that some bugs were delicious. In particular, beetle larvae raised on flour and wine were much in demand among the aristocracy.
The Bible mentions that certain insects are kosher (Leviticus 11: 20-23):
Don’t eat insects that have wings and walk on all four feet; they also are to be hated. But you may eat certain insects that have wings and walk on four feet. You may eat those that have legs with joints above their feet so they can jump. These are the insects you may eat: all kinds of locusts, winged locusts, crickets, and grasshoppers. But all other insects that have wings and walk on four feet you are to hate.
Kosher insects were a significant source of protein in those times. John the Baptist survived in the wilderness on locusts and honey (Mark 1:6).
How unusual is bug-food avoidance, historically?
I think in Europe, the tide started turning against entomophagy in the middle ages. Certain insects are agricultural pests and cause damage to crops. They were often seen as trials sent by God to test the faithful, or as agents of the devil. Vermin (including insects) were taken to ecclesiastical courts and accused of crimes against humanity. They were condemned, and in some cases, excommunicated. See, for example:
or this article (full text on JSTOR):
Such things probably had an effect on the popularity of insects in the diet. But there were also ecological and logistical reasons, that have to do with practicality. In the tropics or warmer climates, insects are much commoner and easier to find, whereas in colder climates it may be harder to find an insect (that doesn't taste foul) in sufficiently large numbers to be worth hunting. Insects are small and much of that mass consists of chitinous exoskeleton. You need an awful lot of insects to justify the time spent finding them in order to justify any nutritional value. This is easier to do in warm climates.
Of course, you could always farm insects to assure a steadier supply, but that raises the level of complexity, and is a bigger barrier to overcome. That said, Europeans have done that too, especially in times of food scarcity.
There are reports of Europeans eating insects from more recent times, for example salted/smoked grasshoppers in Russia, locusts in southern France, both as recently as the 19th century. Beetle larvae were eaten in Lombardy, scarab beetles in Wallachia and Moldova, moths in northern Italy, etc. You can find these examples, and many more, in:
The medicinal use of insects continues to this day in Europe, for example Spanish Fly (canthrides used in various formulations), and head lice. There are other culinary applications, like cheese matured with insect larvae (casu martzu from Sardinia, for example), hung meat (often poultry) that was "aged" until infested with maggots, and considered a delicacy. And of course, insect products, like honey.
It's worth mentioning that crustaceans are also arthropods, just like insects, and Europeans had no problem eating shrimp or crabs, lobsters, crayfish, etc. Many insect-avoiding societies consider these animals dirty in the same way modern Europeans might find beetles or locusts icky. Cultural differences usually account for why societies may make allowances for one type of critter but not another.