Amano shrimp are good tank mates for community fish. They'll ignore your fish altogether. And they eat algae 24x7, which never hurts. Amano shrimp require brackish water for breeding, so won't breed in most tanks. This also makes them difficult to find.
Cherry shrimp (and their color varieties) will also be no threat to your fish. But, they are very small, so aggressive fish (barbs, for example) may go after them. They breed quite easily and rapidly, so if you want more of them make sure you have plenty of hiding places for the young shrimp. Cherry shrimp are also algae eaters, though being so small you'll need huge quantities of them to have an real impact if algae controll is a goal.
Really, for most shrimp in tanks, the issue isn't if they are a danger to the fish, but if the fish will be a danger to the shrimps. Even larger shrimp may find their extremities and tails the target of nipping. The tetras shouldn't be a problem for the shrimp, but the loaches may go after them.
Edit: One heads up about shrimp (and most aquarium invertebrates, actually). A lot of medications and chemicals you might use in a tank are poisonous to them. So once they are in there, you'll need to be extra careful with what you put into the tank, and check that it is safe for shrimp.