Not to say Din is surely the Goddess of the Sand, but the only times we've seen her as more than a golden mannequin kind of thing with almost no features of any kind, it was in a statue where she and her sisters were all portrayed exactly the same and bizarrely had long tongues, and in the little statues on the Triangle Isles. And in the latter they weren't totally portrayed as ideal Hylian women I think, Nayru had fins on her head and all that. But, again, that's not to say the Goddess of the Sand is definitely Din. And if it is, I'd assume the Gerudo were taking creative license.
I disagree! Here's a compilation of how the goddesses have been portrayed throughout the series.
In their first appearance in ALttP, they're potrayed as identical blonde haired, blued-eyed Hylian women.
In OoT, indeed they are featureless golden mannequins but the whole cutscene seems to be metaphorical akin to cutscene in TP where Lanayru talks about the interloppers. In that vision also, Link, Multiple Shadow Links, Ilia, the Triforce, the Fused Shadows appear around a grassy hill in the midst of a pitch black backdrop. All of it was symbolic. I think that's the same thing with Zelda's retelling of Hyrule's Creation Myth and if you think of it has a scene only in Link's Mind, as a boy who grew up in the forest with no knowlege of the outside world or Hyrule's religion, he probably did take the concept "Golden Goddesses" quite literally and imagined vaguely female shapes made of gold. That is not the only definition of golden though. It can alo mean "perfect" or "ideal." In alll other depictions, they're given more details and look like ideal Hylain women.
These are the statues you were talking about in TWW, Yes Nayru does appaer to have fish-like ears but I think this is only maent to be thematic. Nayru is often associated with water so the ears make sense. Farore is associated with forests, plantlife, ect so she has flowers in her hair. Din is associated with fire and has more dragon-looking ears. But all of them look more-or-less Hylian to me. At the very least Nayru isn't exactly a Zora nor is Din a dragon in these depictions. Also it should be noted taht they bear passing resemblances to the Oracles that share their names below.
The Oracles appear Hylian as well. Some argue that Din looks more Gerudo-ish and therefore use that as evidence that Din is a Gerudo Goddess by association but I disagree. While her skin is dark and she has red hair, Hylians can have a wide arrange of skin tones and hair color and besides, she has pointy ears and lacks a distinctly prominent Gerudo nose.
And finally in TP, which seems to reference back to their ALttP potrayal.
As for statues with long tonues, I don't know what you're talking about unless you're referring to the statues in Stone Tower from MM, in which case I never really bought the whole Strone Tower being a big fat "Fuck You" to the Goddesses. They're just creepy statues nothing more. Unless I'm missing something.
All in all, they've been consistently potrayed as Hylian woman unless they've been intentionally simplified for symbolic purposes, such as in OoT. This just makes common sense since the Hylians are their chosen people and therefore would make the Hylians in their own image and likeness. The only other race they could resemble is... maybe the Oocca, since they're supposedly much closer to the Goddesses than even the Hylians but there's been no evidence of that whatsoever. One thing's for sure, Din just isn't Gerudo. Din is a Hyrulean Goddess, and the Gerudo are not part of Hyrule. They're fringe society living on the borderlands betweem the fertile Hyrule and the desolate desert wastes. They've never been part of Hyrule proper and are either depicted as plundering invaders or peaceful nomads. Either way there'd be no reason for them to share the same religion as the people of Hyrule. THe Goddess of the Sands was probably their deity long before they even had any contact with Hyrule and their beliefs.