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?
Honestly, unless there's something wildly improbable going on, the alien bacteria aren't even remotely a threat.
Earth-derived bacteria are a threat to humans because bacteria and humans have four billion years of shared ancestry. They use the same genetic encoding, build their proteins out of the same amino acids, use the same sugars for energy, use the same sort of lipid bilayer to enclose their cells, and so on. That shared ancestry means an Earth-derived bacterium sees a human as a massive pile of resources to eat (and why a human needs an immune system to protect itself).
Now, what are the odds that a random planet's biochemistry is similar enough to Earth's that the bacteria there can consume Earth-derived organic materials? Even a biochemistry based around similar classes of molecules (carbohydrates, amino acids, and so on) is almost certainly going to be incompatible, simply because there are so many possible molecules within those classes.
The biggest threat is probably that the alien bacteria will find your lungs make a great surface to grow on, and proliferate to the point that you suffocate. The odds of getting infected by an alien disease are effectively zero.