It's commonly accepted now that North America was severely depopulated by plague that spread between first contact with Europeans (be that with the vikings or Columbus' expedition, I cannot say) and the political structure of North America by the time of colonization was vastly different before the plagues. I've heard a few scholars say that the reason this happened was because Afro-Eurasians (but more specifically, Europeans) lived with farm animals and became immune to many diseases that wiped out native Americans when introduced. As far as I am aware, the only place in the Americas with large-scale domestication of animals is the former Inca empire, with animals such as the llama and alpaca. And I believe that compared to all other states in the Americas, indigenous Peruvians, Ecuadorians and especially Bolivians make up a larger percentage of the population. Is there any evidence that these peoples were less susceptible to disease when the Spanish arrived due to living with domestic animals?
The idea of American immune systems unable to cope with Eurasian diseases is not generally accepted by those of us who actually study this bit of history.
You may be interested in this post which dissects the myth of the 95% mortality rate from European introduced diseases. To summarize a few points:
That number specifically comes from only certain parts of Mexico, not North America as a whole, and is a total population decline for those areas, including death from other causes.
The numbers come from what were some of the world's densest urban centers at the time, where pathogens spread much more rapidly than elsewhere.
We typically only see major disease outbreaks after some other form of colonialist intervention- Americans were not naturally more susceptible to the diseases. Natives were relocated into centralized settlements, destroying the natural buffers between centers that impede disease, were intentionally starved, increasing susceptibility, and were often subjected to intense physical labor, furthering weakening defenses.
That doesn't have too much to do with animal domestication theories. So what of them? Meh. Jared Diamond's the biggest proponent of them, and he's neither a historian, biologist, or anthropologist. There are 5 main diseases the theory proposes jumped from livestock to humans. Three of these are not "compatible" with both humans and animals and couldn't have made that jump, and there's good evidence that the other two were troubling humans before they were intensely domesticating cattle and the like.