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So, let's say you have two planets in parallel universes. Travel is possible between Earth and the second planet via wormholes or whatever (not important). While the oxygen-nitrogen-et cetera ratios and air pressure are similar enough to be survivable by both species, there remains the issue of bacteria. Earth's atmosphere is chock full of all sorts of diseases that we don't even consider diseases due to our natural immunity or their tendency to infect things like plants or dirt or fish instead of humans, but then stuff like the common cold is known to kill gorillas apparently. Of the bacteria in Earth's atmosphere (discounting staph), how many of them are likely to actually be deadly to someone with a human-like immune system that's never encountered them before? Worst-case scenario, someone runs out of their own air supply and has to take off their helmet and breathe the local air to avoid suffocating immediately. How boned are they?