“Redwood are algae” is a similar statement to “Pterodactyls are fish” or “bees are crustaceans”. Redwoods are land plants, thus are also members of Viridiplantae - the clade containing land plants and green algae. The sister taxa to Viridiplantae in clade Archaeplastidia are Glaucophyta (unicellular algae), and Rhodaria (contains red algae among other things). Thus since land plants are more closely related to green algae than green algae is to red algae or glaucophytes, if we want to treat the term “algae” as a monophyletic clade, then we have to include land plants in that, which of course includes redwoods.