Respectfully OP while I understand where you're coming from, it's still a boundary fence and your neighbours can't be forced to look at the algae just because you erected the fence.
I guess if you really wanted to get legal you could sue them?!
A more practical solution though would be accepting that it's unfair on your neighbours to be forced to look at algae infested fence posts. It would have been better if they asked you first but they didn't. Hardly the crime of the century, and hardly anything worth falling out with the neighbours.
The practical solution that avoids awkward conversations is to paint over just the offending posts. Go for a mid-dark green colour so that it will blend with your algae infested panels (I'm not having a go! This would blend best) but it will also satisfy your neighbours in the sense that it will be paint they're looking at, not algae
As an aside, I get that you have lots od fences but I wonder how your neighbours feel looking at algae posts but not being allowed to paint them, while you're also refusing to paint them
It's not great sadly and while you might (?) have the legal bit on your side, it's not very neighbourly of you to just say "nope, I prefer it shabby, I won't paint it, and you're not allowed to paint it either cause it's mine" because it's not nice to be forced to look at something that's unsightly