As u/Red_AtNight mentioned, most nightshades are in someway poisonous. I'm not a botanist so I can't say they all are, but most are, especially the wild ones.

We've domesticated things like tomatoes and potatoes but even potatoes can be highly toxic if you eat too much of the wrong bits. I believe they are also a kind of toxin that likes to stay in your fat tissue so it can accumulate slowly over time.

I'm not sure about which diets avoid nightshades other than Macrobiotic diets which as far as I know are more based eastern philosophy rather than some sort of nutritional logic. For example, the Macrobiotic diet classifies foods according to their status in a Yin/Yang balance so certain foods can only be paired with others in a dish. Specifically the nightshades are excluded from the diet entirely, again for philosophical reasons, not for some actual nutritional or ethical logic.

There might also be a religious aspect, I believe the early European colonists believed the tomato was the supposed "Biblical Fruit" that Eve ate and so they believed it both kill you and then damn you hell if you ate it. Obviously that didn't last long. FWIW, I think 'scholars' have since agreed the fruit was a quince.