We would probably poison alien bacteria etc, and they would poison us.
So we just walk around. The alien life would probably sample us. We have mosquitoes, mites, nematodes, and various other things that get under our skin. Presumably the alien ecology has similar things. They inject us with -- stuff. It happens a whole lot here, and if we have skin exposed, it will happen there. We'd breathe things too, exposing our mucous membranes to them. And lungs some. We have defenses to keep living things we breathe in from hurting us much. Those defenses would not be as necessary -- the alien life probably can't live in our lungs etc -- and also partly ineffective.
So stuff gets into us, and the live part of it will tend to die there. Some of it is just -- stuff. Saliva, excretion products, whatever.
We would be randomly allergic to it. We have developed allergies to things already, things that correspond to not-self stuff we have been challenged by in the past. And they might randomly correspond to alien stuff.
For example we have antibodies. These attach to anything that's the right shape with the right locations of hydrogen bonding etc. Something can fit imperfectly and still fit well enough to get a reaction. The region they fit to (called an epitope) tends to about 8 to 17 amino acids long. Sometimes it's a specific sequence of amino acids that has folded up just right, and other times it's two or more sequences that have folded with each other.
Alien proteins or other alien molecules would fit some of our antibodies. So we would react. We would itch etc. It would be a continual irritation. Probably we could mostly live with that.
Would some people occasionally die of anaphylactic shock? Maybe.
We might easily become allergic to foreign stuff. I think it would happen particularly if we get exposed to it and get problems, about every 2 weeks. Continuous exposure I think would result in less allergy. Maybe. If it's always around and usually doesn't cause trouble, it's less allergenic than if it shows up along with trouble, at 2 week intervals. So that's one thing to be careful about. Arrange the times of exposure to minimize allergies.
I'm not sure what else to say. Some of the foreign stuff might be very poisonous, and I see no way to tell which would be. Some of the foreign DNA might be highly mutagenic and carcinogenic. If your body's DNA-building machinery mistakes foreign nucleic acids for regular nucleic acids, it might incorporate them into your DNA and then mis-copy them the next time the cell replicates. That can be very bad.
Or they might interfere with regulation of various kinds. If your cells mistake a foreign amino acid or nucleic acid for one of your own -- just by the proteins that shut down production when there's too much -- then it could stop you from making stuff you need. Which you could have made plenty of if the signalling wasn't screwed.
There are lots of ways for things to go wrong and some of them could be pretty subtle. You might go years before cancer shows up, or months before you get deficiency diseases of various sorts even though whatever you are deficient in is plentifully available in your food or even in your bloodstream.
Lots of unpredictable effects possible. It might be possible to get lucky and none of them happen. Luck of the draw.