Waste leaks from the lavs is blue in colour and typically freezes to a blivet of seveal pounds at altitude only to shear off when the aircraft skin warms up.
Your description would rule that out.
Bird poop in the air breaks up into white not brown droplets. To prove this just stand on a boat fan tail or poop deck of a ship and throw some fishing chum to the gulls. They will process it and give you back a favour.
I suspect that what you may be experiencing is the outfall of some smokestack upwind.