Yes, when used as directed, algaecide is safe for fish and plants. However, there is an exception. Algaecide is toxic to aquatic invertebrates which include some species of fish and crustaceans. Aquatic invertebrates do not have a backbone or spinal column. These include earthworms, sea stars, sea urchins, jellyfish, squid, snails, lobsters, crabs, shrimp, etc… There are a few classes of fish that are also invertebrates, such as Jawless Fish (Class Agnatha) and Cartilaginous Fish (Class Chondrichthyes) which don’t have a true backbone, instead, they have a skeleton made of cartilage instead of bone.
Learn more about aquatic invertebrates and cartilaginous fish from these online sources: