I forgot to add some other considerations:
If you plan to spend a lot of time in the birdcage look into sun reducing screening, we have 75% sun reducing screening in the roof area only. This works great, acts like a slightly cloudy day so it provides shade and keeps the area cooler while still allowing air to circulate. Also, if you are concerned about privacy the white (or light colored) screening will tend to block people from seeing into the bird cage during the day, the opposite will be true at night if you have lights on in the birdcage.

Our house had a white pool cage and, as other mentioned, it looked old and dirty.

I had Mr. Pool Screen in Orlando paint it with Sherwin Williams Bond-Plex in 2022 and it still looks great today. The color is Urbane Bronze 820433 if anyone is looking for it.

Totally agree, but most bird cages I see have high roofs with high sides forcing people to use awnings and umbrellas.
So those sun reducing screens would benefit the side walls also.

DARK!!
In 1999 we built a house in Tampa and put in a white birdcage around the pool.
BIG mistake!

If your white screen is ok with the property owners that need to view your birdcage then fine. I think a white screen can look a bit "too much" especially at night. Your choice.