How to keep bird bath clean

Mine is the same. I think some of it is the debris which comes from the birds' wings. You've just reminded me to go outside and clean mine! Lovely to see them enjoying the water isn't it.

The top of mine can be lifted, so I bleach it, then rinse it thoroughly, and refill with clean water every few weeks.

I read yesterday to clean it with vinegar, give it a good brush followed by lots of rinses.

We put diluted hydrogen peroxide in our fountain and bird bath, it completely harmless to the birds and keeps both algae free.
Dilution is roughly one tablespoon to a gallon of water.

It’s Haematococcus pluvialis which is a freshwater species of chlorophyta (green algae). The red orange colour comes from the antioxidant astaxanthin which is believed to protect the algae from the detrimental effect of UV-radiation from direct sunlight.

Natural sources of astaxanthin, as well as in algae, are in yeast, salmon, trout, krill, shrimp and crayfish.

Keeping the bath out of the sun will help reduce the growth of algae but it will keep coming back as birds will carry it on their bodies from one water source to another.

I wouldn't use any chemicals on it, vinegar or bleach as any residue could harm the birds or another animal or insect which drink there. Just rinse it out and scrub with a coarse brush if necessary.

Thank you all for your suggestions.