I think mostly it's the opposite of what you describe. Diversity is key here, because if everyone had all those same molecular markers, we'd all be susceptible to the same virus. Mixing things up gives the species as a whole a better chance to survive a bad pandemic, if there are some groups that will be relatively safer (because their cells are harder for the virus to infect, or their immune systems start with proteins that will be better able to adapt to that specific virus, etc.). Certain genotypes and haplotypes confer more (or less) susceptibilty (or protection) to some viruses and this would likely be the case with anything "new" that crossed over from another species. It's all really complicated and of course we're all anthropomorphizing species and viruses and cells and proteins because it makes it easier to understand. Evolution is wild.

On a side note, cheetahs are really lucky. There is an incredibly small amount of genetic diversity in the cheetah population--to the point where I've read that any cheetah can get an organ transplant from any other cheetah. One study gave convincing evidence that the total population at one point was down to something like "no more than 7 individuals"... especially at that extreme bottleneck point, but even up to today, it would seem that they may be more susceptible to an extinction-level cheetah pandemic. Something like that could happen to humans, and things would likely be pretty grim, but our diversity could mean a better shot at existential survival in such a scenario.