Buy a coconut in the supermarket. What's the color?
The "nut" is most likely brown and hairy. Sure, it's not like they appear when still on the trees, but who knows?
IMO it's all about being recognizable (and also knowledge) to some extent.
In a similar way, if you see Bananas in a cartoon, they're yellow. Tomatoes are red, apples are typically red, etc. even though these things will most likely have a different color or more variation while still being on a plant.
I think you could even go a bit further and compare this a bit to space fights in fiction: Explosions, sounds, pew-pew-pew, etc. yet you shouldn't hear anything. It's about what people know and recognize, it's not about what's realistic.
If you want to, you could even consider brown coconuts to be stereotypical coconuts! :) As a different example, what's been the last time you saw some Bavarian in a (non-serious) cartoon (e.g. looney toons)? Chances are high, he had some traditional costume on, at least some lederhosen. I'm from Bavaria, and I've never worn a lederhosen (since being like 3 or 4 years old; didn't have the choice!). Yet as some caricature I'd most likely have one on me - not to forget a Mass of beer in my hands.