Where did the other races (and genders) go?

Elves: Self-imposed exile

A history of the elves was released for the canceled game Ultima X: Odyssey. In that, it says that they chose a self-imposed exile from Sosaria as a result of their failure to stop Exodus from coming to power in Ultima III, and the resulting cataclysm that transformed the face of the world.

The elves were mortified that they had allowed this fate to befall the land they strove to protect, and the general belief was that they had failed utterly. Many of the older elves, as well as most of the ruling council, felt that atonement for such a heinous failure was impossible, and believed that their only option was to leave Sosaria in shame. […]

One emissary from the high council was sent from the elven city to meet with the humans. As he traveled, he was shocked by what he witnessed. Fields were gone, replaced by jagged, gaping chasms where the earth had been ripped apart. Mighty trees had been reduced to piles of kindling. Many of the inhabitants of small villages had not made it to safety before Exodus's evil had taken its toll. The elven emissary saw all this, and was horrified. […]

The emissary returned to the council with the invitation, but he also shared with them what he had seen, in all its horror. Hearing this, the ruling council was so racked with guilt over their failure to protect the land and its inhabitants, that they made the gut-wrenching decision to leave the world of Sosaria. Quietly - so quietly that history never recorded when it happened - the elves left Sosaria in self-imposed exile, never to be seen there again.

Part of the plot of Odyssey was to have been that some of the younger elves felt they had a duty to atone for their failure in Sosaria and so they reach out to aid the Avatar.

Dwarves: Intermarriage with humans

Ultima Underworld includes a colony of "Mountain-Folk" led by Goldthirst. The book "Memoires of Cabirus", which was included with the game, explicitly says that they were once known as "Dwarves". According to this, the dwarves assimilated into other cultures, and Goldthirst's group is one of the only ones left keeping their original identity.

Short of stature and broad of shoulder, the Mountain-Folk - known in times past as "Dwarves," though they detest this name - have a unique lifestyle dedicated to traditional craftsmanship. Over the ages, however, their distrust of outsiders and their well-known love for precious metals have put them in disrepute. In the past century, many of the Folk abandoned their old ways, left their homes, and married outside their clan.

I was surprised when the Chief of the Mountain-Folk wrote to me con- cerning the desire of his people to join the Abyssal Colony. Knowing that the Folk were in danger of dying out as a culture, I suggested that the Chief might not want his people to be part of our town - where, after all, our goal is to prove that all people can live in unity.

Bobbits and Fuzzies: Unknown

No information is given for why the Bobbits and Fuzzies no longer exist after Ultima III. It's possible that they too were affected by the cataclysm that resulted from Exodus, or that they also intermarried.

However, the fan remake The Ultima 6 Project (a mod for Dungeon Siege) includes a band of Fuzzies and their chief, Porshon, provides this explanation:

Porshon told the hero he had been born shortly after the fall of The Destroyer, Exodus. In those days, the fuzzies had been numerous, and had lived alongside the humans and other races in the Big World. With the fall of Exodus, his people lost their link to nature, and began to decline in number. They were only saved by the appearance of the Helpful Lights, the wisps, who helped restore the lost connection for the fuzzy people. The wisps taught the fuzzies about the Silver Petal trees, or silverleaf, and how to cultivate and care for the trees, which provided a home and a future for their race.

_{–The Ultima Wiki}

This explanation suggests that the Fuzzies became the Emps that appear in Ultima VII, especially since in both that game and The Ultima VI Project, they only talk with you if you bring them honey.

In the official games, the Fuzzies and the Emps are both small, hairy humanoids who are proficient in magic, but no link has been established between them.

The "Other" gender

Ultima III is the only game in the series that allows you to choose a gender of "Other" (Ultimas I-VII allow you to be either male or female, while VIII and IX require you to be male). I cannot find any reason for this removal, but if I were to guess, it wasn't for a story reason but rather a technical reason.

"Other" can mean a lot of different things to different people, and it adds additional complexity to NPC interactions. For instance, how do you handle talking to the people in the brothel of Buccaneer's Den if your gender is "Other", and how much more time and effort will it take to write and program that? I suspect the designers didn't want to open that can of worms, or spend as much time on that feature, and just decided to remove it (and given that Ultima IV came out in 1985, I don't think there was a lot of demand to keep it in).