So feeding wild insects to reptiles is bad because they could carry nasty things like parasites or pesticides. But would it be safe if I caught some of them, bred them, and kept the offspring separate from the wild caught crickets? I would imagine that would be enough to get rid of the risk of pesticides, but would it get rid of parasites? Are there other risks that can be passed on from the crickets to their eggs?
Not safe: Parasites can infect the offspring of the host they live in. The chemicals from pesticides (or anything, really) can also travel to the reproductive organs of whoever ingested them.
I know the question clearly states crickets -> eggs, but you can apply this to any living creature. The blood and nutrients are passed down from the mother. Anything affecting the mother will always affect the child.