The DE, diatomaceous earth, is effective against crawling insects that rub over it, like ants and silverfish. It also works against slugs and snails. It won't harm your praying mantis, which walks above it on tall legs.
The Bt, bacillus thuringiensis, is used because it is host specific. It targets only the larvae of leaf-eating lepidopterans (moths and butterflies). The hornworm is the larva of a moth and would be eradicated by it, but in the process you would also lose swallowtail and other butterflies you might like having in your garden. But the praying mantis would not be harmed.
Here's a reference:
Because of its specificity for leaf-feeding Lepidopteran larvae,
the B.t. formulations commonly used in forestry situations have
not been implicated in other non-target insect deaths. Honey
bees, stiltbugs, flies, and beetles all show few or no effects
from spraying, and praying mantis and earthworms were not
adversely affected(5). However, one study noted a reduction in
the number of some parasitic adult wasps and a Lane County,
Oregon study indicated a two year reduction in the numbers of
non-target Lepidoptera, but noted recovery by the third year(16).
Grasshoppers will not be harmed by either the Bt or the DE, so you would still have them. Here's a reference re organic control of grasshoppers:
Predators include snakes, toads, cats, mice, a number of birds (bluebirds, sparrows, mockingbirds and others), chickens, ducks, geese, spiders, horsehair nematodes.
Barriers: grasshoppers are said to be repelled by horehound, cilantro, calendula, garlic oil, and nitrogen-fixing crops like peas and sweet clover.
Row covers, like Reemay, or screens can be effectively used to keep them from your crops.
Garlic Oil Spray
To make: Combine 3 ounces of minced garlic cloves with 1 ounce of mineral oil. Let soak for 24 hours or longer. Strain.
Next mix 1 teaspoon of fish emulsion with 16 ounces of water. Add 1 tablespoon of castile soap to this.
Now slowly combine the fish emulsion water with the garlic oil. Kept in a sealed glass container this mixture will stay viable for several months. To use: Mix 2 tablespoons of garlic oil with 1 pint of water and spray.