Well, there are lots of different shades of pinks (from candy-colored to fleshy, to reddish to almost purple) and they could be multicolored too (like having blue limbs) seeing how they‘re made up of blue horrors anyways… in various artworks (and the background) they‘re much more varied than the minis by the Eavy Metal team. Some, like the Silver Tower sculpt got painted more interestingly too.
The classic colors for each God are the typical choices but frankly you can paint a chaotic force however you please. Yep, blur or green or red or purple might be the go-to choice but those colors are not set in stone, usually just a form of superstition (as in lucky colors) and frankly have been modified, expanded upon and changed over the years anyways.
So paint them however you want. Does it look strange to see green bloodletters? Yup, it even feels off after so many years of indoctrination. There‘s an established look for things but doesn‘t mean they have to be painted like that. I doubt Khorne would care, so why would you? Can‘t expect people to like it though but who cares, those are your minis.
I think in some cases, like the one you’ve given, where you field a unit that is named after a color like Pink Horrors or you play an army with an established color scheme it feels a bit off but even within the confines of the background there is lots of room for creative paintjobs in those cases. They could just have pink flames or eyes. Limiting units of Tzeentch to any color feels pretty off anyways. „Disrespecting“ the lore might not be appreciated by others but if that‘s the case, try to play with other people. I‘d rather play against pink goblins if it makes my opponent happy. And they should be greenskins in theory. But invent a decent reason why they are not (might some pigmentation-mutation due to some rare shrooms and you can appease even fanatics of the lore and got some cool story for you army to boot. Dunno why people lament it, GW has always been pretty open about colors.
There‘s only one solid exception in a tournament setting and that is when you paint e.g. your marines as another chapter than the one whose rules you use. I mean, explaining it would sort that problem too in like 5 secs but it is what it is…. So don‘t worry and mock the people that can‘t get over you painting your minis differently if needed! 🥳