The verdict for each tankmate
Snails first, because they are the easy half of the question: nerite and mystery snails are safe with black skirt tetras. A tetra may investigate a snail's antennae once, learn they are not food, and lose interest; the snail's shell handles the rest. Shrimp need a split verdict. Adult shrimp - amano shrimp especially, and full-grown cherry shrimp - are generally left alone by black skirts, which are mid-water schoolers rather than dedicated hunters. Where the pairing genuinely fails is one size down: newborn shrimplets are exactly the size of the live food these tetras evolved to snap up, and no temperament on the tetras' part will change that.
School size is a safety feature
Black skirt tetras carry a mild reputation for nipping, and it is almost entirely a numbers problem. In a pair or trio, the school's social energy has nowhere to go, so it gets spent pestering tankmates and testing fins. In a proper group of six or more - and ten is better still - that same energy stays inside the school, in chases and displays among themselves, and the shrimp and snails fade into background furniture. If you are planning this combination, buy the school the tetras need before you judge their behaviour; most 'incompatible tetra' stories are understocked-school stories.
Engineer the shrimplets' escape routes
If your shrimp are breeding and you want babies to survive, build the nursery into the scape rather than hoping for mercy. A dense clump of Java moss, a thicket of fine-leaved plants and a pile of small stones or cholla wood give shrimplets somewhere a tetra's mouth cannot follow, and most will spend their first weeks inside that cover, emerging as they outgrow snack size. Feeding the tetras reliably, at the surface and at set times, also matters: a hungry school hunts the whole tank, while a fed one mostly waits for the next meal to arrive from above.
Set the order of arrival
Sequence helps the shrimp's side of the bargain. A colony established first - settled, grazing confidently and already breeding into good cover - weathers the arrival of tetras far better than shrimp added to a tank where a tetra school already owns every sightline. Add the tetras last, add them as a complete school rather than in dribs and drabs, and watch the first few days at feeding time, when excitement runs highest. The occasional curious peck at a large shrimp is normal; shrimp that stop coming out to graze at all are telling you the balance needs adjusting.
One stocking plan everyone can see
Combinations like this one unravel at the shop, not in the tank: someone in the household falls for a personable little predator, or adds two more tetras' worth of something nippy, and the careful balance is gone in an afternoon. The fix is a stocking plan that lives outside one person's memory - who is in the tank, who is planned, and which additions are ruled out and why. For the tetras themselves, relatives you pick can open the tank's profile once you grant them access through Family Sharing in KinsLe.