As tmv said. Just take the seperation of eukaryotes and prokaryotes, which didn't happen too long ago. But a virus that attacks a bacterium has no effect on us. And in the life-came-here-on-a-comet-scenario, the split between life on earth and aliens happened a few billion years before that.
We may also find that life tends to evolve down similar pathways as a matter of chaos theory. It may be mathematically 'natural' for a creature like a deer or a human to emerge from the pool of life that does what it does naturally over time, seeking new forms of physical expression and finding limited numbers of highly successful expressions, all for similar reasons. The same may happen at a fundamental microbial level. AKA, simply because life IS life, it is all more closely related, wherever it may be found, than we may imagine now from our position of lacking observable phenomenon at this time regarding the subject.
The fact that Native Americans were decimated by something the rest of the world sniffles at is one of those things that may end up becoming an even more powerful effect when the races of previously isolated planets meet and mingle.
The real question here would be: Are diseases still relevant when we get in direct (physical) contact with alien life? Sure there is a chance that as I write this, there are aliens approaching our planet, but this chance is extermely small. It is much more likely that the first alien-life we encounter is primitive, so WE would be the party that travels there. If we assume there is no alien life in our solar system, it would take humans at least 50 years to get there (probably much longer). Within 50 years, it is predicted to develope smart medicine, iE Nanobots, that have the potential to cure every transmittable disease.
Whether we have amazing medical technologies or not, we're going to need an equally amazing answer to our current fabric of economic Darwinism to ensure that all have access to the highest level of care. The societal elites on Earth currently would prefer that we were about 80% less populated and once we have truly replaced most professions with automated capabilities, which we are currently racing to achieve, the purpose of maintaining such huge herds of human beings as we currently do is going to be gone, leaving the vast majority of us incapable of finding employment to support ourselves at all, let alone provide ourselves with any level of medical care whatsoever. So while we may be able to ensure the absolute longevity, perhaps even indefinitely, for the ultra rich, the rest of us will likely see an absolute nose dive in life expectancy and certainly would not see access to such 'smart medicine' technologies, not unless we begin to rapidly colonize space and give ourselves another way to relieve the planet of its burden. But before even then, the elites would likely wish to first refine our species genomically and eliminate those lines that do not prove capable of surviving in a much more limited environment of economic access. AKA, we're probably about to be starved off here folks. Those that survive the next 100 years will inherit the technologies to enable effective immortality. The rest of us may find that in a more spiritual sense if we're lucky enough that some religions are true.
Also, to respond to one point you made in there more directly:
Sure there is a chance that as I write this, there are aliens approaching our planet, but this chance is extermely small.
My worldview states that it is not unlikely but rather that 'they' have been here all along and we are silly apes who merely THINK, because that's what they want us to think, that we are a species vastly isolated from the rest of the galaxy. Truth is, we've been little more than an owned colony since our origins. That's the power of propaganda for ya.