Given how humans back in the 1840s viewed race, it would likely be even more of a mess. This is especially significant since your story involves a British Colonized Sicily. Your story would have been set around the same time as the Irish famine, and what happened to the Irish is partly due to the English belief that the Irish are "inferiors" or "savages" who cannot be civilized. The English were practically the first to develop our modern idea of race, in fact, they used the idea of race to separate humans into separate species.
Do take note that even though the Irish were light skinned, they were not considered "white" by the English or Americans. Given their historical treatment, it would be pretty terrible to be a native Sicilian under British rule since you're not only Catholic, which would make you the target of discrimination under Protestant rule, but you would not be considered "white" at all, you would practically be considered some isolated sup-species of Italian in the eyes of the English. I wouldn't be surprised if your setting has anything similar to the Irish Potato famine in Sicily, which would result in Sicilians immigrating to places like mainland Italy, Britain itself, or even America in order to escape the struggles.
How would this extend to fantasy races? Well, it depends on which races are present. You used Elementals, Dwarves, Elves, and Beast kin as examples, so I'll use them as examples as well. Since this is long before Tolkien and his adaptation of Nordic Elves, the English would probably have a very different view of Elves compared to us modern folk. The most likely association the English would make would be with the Seelie and Unseelie Fae, who are often portrayed as unpredictable and unreliable aliens that just so happen to look human. So, Elves would actually be subject to discrimination because of the belief that they're Fae and you don't know what they're going to do. Dwarves would honestly be seen in similar ways to Jews and Irish. Not only would their value for hard work draw the ire of English workers who would accuse them of taking their jobs, especially in industrial and mining jobs given their short statures would have advantages compared to the common man, but their association with gold would make the English think the Dwarves are naturally greedy.
And that's just for the races that look human, for races like Elementals and Beast men, the English wouldn't even really recognize them as sapient beings. If we were to include other fantasy races like the Orcs, they would either be considered a missing link between apes and men, even lower than the African depending on how Orcs look. While at this time the English Empire was cracking down on the slave trade hard, it is unlikely that the abolitionist movements of those days would have included the races that barely look human under their umbrella.
Now this answer is mainly going off of how the English would see race since we have the most information about how they saw other groups. I'm not sure how reliable Britannica is considered here, but here's a link to their website for extra information. Britannica Race History One of the things it mentions is that even by the time of the mid 1700s, Linnaus had four major subspecies of humans listed: H. americanus, H. africanus, H. europaeus, and H. asiaticus, with anything that didn't fit those four categories listed as H. Monstrosus and H. Ferus for the exotic peoples and wild men respectively. These latter two would probably be where most of our fantasy races would find themselves in unless certain races either got their own categories, like Dwarves being H. Rotundus and Elves being H. Elvenus. There is also the possibility that some members of certain humanoid fantasy races would try their best to claim that they're part of the civilized human race, or "white" race. Such as some Elves trying to claim that they share a similar heritage to the Anglo-Saxons in order to escape persecution and discrimination.
So, to summarize, if Fantasy Races existed in a British Controlled Sicily in the 1840s, there would still be racism as we saw it progress into modern day, only this time most humanoid races would find themselves in the middle of it as well, and the non-humanoid races would be very unlikely to be seen as anything equal to a human.