For post #32981 I can tell you they were unintentionally using the incorrect VAE as someone pointed it out to them on 4chan since they wondered why it was coming out desaturated, and they later fixed it, as can be seen from the rest of their work afterwards. I'm willing to bet it's almost always unintentional, but it would be correct that it's not always the case though and it is situational.
The 'Anything' titled vae(s)
These are almost always the NAI VAE renamed (not the same as the SD 1.0 VAE). You can verify the hash of these yourself. This is technically the "correct" VAE to use for anime artwork, since it was presumably trained on it, though we don't really have a way to verify this as it's from a leaked source, but users often use the newer SD VAEs or Waifu Diffusion VAEs because those produce more saturated colors.
vae/no vae
Also want to point out there is no such thing as "no vae", as the image would be stuck in latent space otherwise. This has became the colloquially used term for it because it's simpler and easier to understand in comparison to "SD 1.0 VAE" though. Most users don't even know the purpose or possibly the existence of a VAE though, which is another reason I believe this is almost always unintentional.
I will see if I can do some analysis to find more images based on their color range. My personal assumptions are: if the image is desaturated, and metadata is fully intact, it's almost always a case where the user is unaware of the problem. If the image comes from a source where metadata is kept (such as Pixiv) but there is no metadata, and it is desaturated, then it may be intentional.