I don't think the green algae poses a thread to the birds. The easiest way to get rid is scrubbing with a brush or sponge. My rule of thumb: when my waterer turns green it is time to clean!
Though many types of algae are harmless to birds, a few are deadly. In addition, if you happen to get some forms of cyanobacteria at high concentrations, it can be toxic too. You may be lucky, but maybe not! Keeping waterers in the shade helps, and I find that the plastic ones clean out more easily in summer. I watered the chickens indoors and didn't have any this summer.
Reading this makes me realize how much I've learned from reading this forum!
What I've read: one generous tbs apple cider vinegar (with "mother") per gallon.
My birds go through about 3 gallons every other day, but I am sure to dump the trough and get rid of any debris _every_ day. When I fill it, I scrub and hose off the whole waterer. No algae yet!
I know some people suggest cleaning with bleach, but I've got to say that I have chosen not to do that. I have yet to make my peace with bleach