I was gonna throw this in tags but it's lengthy and an interesting social point in the story.
My favorite example of Gridanian racism is the dude sitting right next to the aetheryte plaza, who will comment to anyone that passes by 'just what we needed, another outsider'. And if you go around the city, you'll catch a few other instances of citizens or guards harassing or insulting miqo'te or Duskwight elezen. In various conversations and quests, the Adders in particular do not hesitate to express their hate of these minority groups, preferring a brutal 'hang 'em now and let the gods sort 'em out' approach. Yet it seems so senseless. Aside from attacks by the Ixal, the Shroud appears to be a fairly peaceful and abundant realm with a banditry problem.
While they comment on it somewhat, a key part of lore that is missing for Gridania and not expressed enough in the modern story is their intense fear of the Elementals. Since the end of the War of the Magi some 1,500 years ago, the Black Shroud had been controlled with an iron fist not by men but by the Elementals. Both elezen and hyur had been driven underground and lived in the city of Gelmorra for centuries before conjurers finally developed the means to communicate with the Elementals, who allowed gradual settlement of the Shroud. But the Elementals had rules. Strict rules. Failing to follow the Elementals' rules would result in Greenwrath, which could manifest in a few ways but was more or less an instant death sentence by the forest. No one was exempt. Even the dragon gets in trouble. The Elementals could also punish communities or humankind as a whole if they misbehaved in the Shroud, influencing food yields, health or sickness, and the behavior of monsters. So the Gridanians, with the Padjal as speakers for the Elementals, quickly learned: the Elementals will must be followed, regardless of mortal needs or wants, and anything that threatens the balance must be eliminated.
In this regard, I feel SE doesn't really do a great job in 2.0+ at conveying how absolutely terrified the Gridanians are of the Greenwrath and how the Elementals' decisions shaped their entire society for hundreds of years. Yes, there are NPC comments and side details that you can use to piece things together, but it is tricky, and often doesn't provide great context. After 2.0, the Elementals are almost completely gone, and the threat of Greenwrath with it, but society doesn't change overnight. Once, if you had low crop yields, you simply had to tighten your belt and accept that you were going to be hungry. Trying to poach or forage for more food could piss off the Elementals. You were part of a marginalized group, like miqo'te or Duskwights? You either had to suck it up or leave the Shroud completely. No housing opportunities? Sorry, we've already hit our logging quota for the year and have none to allocate to you, shit sucks. But post-Calamity? The inequality and sorta-authoritarianism forced upon mortals by the Elementals no longer exists. The poor, the downtrodden, the minorities, the bold and the desperate can all seek their own salvation out in the Shroud once they figured out that Greenwrath wasn't being enforced. Gridania didn't help them before, and the Calamity only worsened conditions, so they must help themselves. But to the Gridanians, conditioned by centuries of following the Elemental's edicts, these are not fellow citizens, clearly suffering and in need of aid. These are lawbreakers, criminals, threats not only to society but to the very lives of everyone in the Shroud. The way the Gridanians see it, 'oh the Elementals might not have smote you on the spot but they're keeping count, and they'll kill us all if you don't stop defiling the Shroud. So instead we'll kill you first'.
And unlike Limsa or Ul'dah? They don't really seem to be moving away from it either. Does it justify the racism and various social woes, especially post-Calamity? Nope. Does it at least explain why Gridania is almost comically racist and authoritarian? Yeah.