I like the references for Risky Boots, Toriel, and Esmeralda’s goat.

@Snicky  
Ah, another sea shanty. Probably means no color reference to anything then. I’d say they’re definitely assigning shanty lyrics to palettes that are just meant to be cool recolors and not pop culture references.
 
As for the other two, good catch. I wouldn’t have got those.

@FanOfMostEverything  
It makes sense given her wall-cling thingy.

@ScyStorm
 
What Shall we Do - with a drunken sailor?
 
Akerbeltz - colored based on a mythological goat creature of the same name
 
Miracle Courtier - Based on Esmeralda and her goat from The Hunchback of Notre Dame

Do note that Shanty is likely to have more palettes than this on release, and also the silly names given here are subject to change.
 
As for what they reference (EDIT: Thanks Snicky!):
 
Shanty = it she  
Ditty = Name means “a short, simple song”; colors likely don’t reference anything  
What shall we do = Name references a well-known sea shanty; colors likely don’t reference anything  
D’ja make ‘er? = Jamaican flag  
And a bottle of rum = Name references a well-known sea shanty; colors likely don’t reference anything  
Akerbeltz = Mythological goat creature  
Teal Suede = Ugly tennis shoe (all characters have this palette)  
GoatMom = Toriel from Undertale  
Shout of Sea = WoolieWoolz, aka WoolieVS, streamer/youtuber  
Lightning Rival = Absa from Rivals of Aether  
Jellyfish Pirate = May from Guilty Gear  
Grass Pelt = Gogoat from Pokemon  
I’m so sorry = Kai from Kung Fu Panda 3  
Miracle Courtier = Esmeralda from Hunchback of Notre Dame  
Dangerous Hoofwear = Risky Boots from Shantae series  
Island Villager = Sherb from Animal Crossing  
Super Bleat Kid = Meat Boy  
QLR:D = Predator Shadow (all characters have this palette)

@Background Pony #F82D  
The colors don’t match for that

Is “I’m So Sorry” an Undertale reference?

Is “QLR:D” perhaps related to Goat Simulator?

@Background Pony #8526  
At least not yet.

No Guybrush Threepwood skin ?

Shout of Sea looks to be Woollie Madden from Super Best Friends Play

Is jellyfish pirate May from guilty gear?

I was not expecting a Super Meat Boy reference.

I see Dangerous hoofwear = Risky Boots

I see the Toriel= Goat Mom and Absa=Lightning Rival references.