Of course diseases still existed in hunter-gatherer societies, they just didn't have the capacity to spread as far. If, for example, during COVID, everyone had formed groups of say 100 people and those 100 people only ever interacted with each other, that would have made it very difficult for the virus to spread. Obviously, that's impossible today because we are too interconnected, but that was more or less how hunter-gatherer tribes tended to function.

Disease wasn't a significant limiting factor in the size of those groups because there were other limiting factors. One is resource availability. Without agriculture, what the land naturally produces is what's available, and larger groups would require more resources. Another factor is social dynamics. The larger a group is, the less likely you are to personally know everyone in the group. Informal collective decision making also gets harder as you scale up, with smaller groups, it's possible for everyone's concerns to be heard and accommodated.

The extent to which xenophobia is a product of nature rather than nurture is debatable. I would argue that racist attitudes are taught and passed down, usually informally, rather than being innate. Growing up, I learned one set of stereotypes about Japanese people and another set of stereotypes about Chinese people. The origins of those stereotypes can be traced historically, and it's not as though everyone comes up with stereotypes on their own and they just happened to arrive at the same ones.

I would say the thing that is more evolutionarily ingrained in us is "Dunbar's Number,", which limits the size of our direct social in-group to around 150 people, likely consistent with the size of hunter-gatherer tribes. Modern ideas of race or nationality obviously present an in-group that goes far beyond that number, which suggests that those ideas are learned rather than innate. There is a degree that we have to be taught how to function in a world with regular interactions with strangers in general, but I would argue that treating people differently based on race or other characteristics is learned behavior. Though of course, everyone starts in a state of ignorance and ignorance of someone's culture can lead to accidental offenses and misunderstandings.