Yes the atoms and basic organic molecules (Carbohydrate, amino acid, ethanoic acid ...) are universal.
But the infection is protein-dependent. And proteins are species-specific. Tell me what protein you produce and I will tell you which kingdom you are. Collagen is a typically animal protein. Distributed everywhere in all animals. From the sea sponge to the jellyfish to the ants, the snake and the man. It has not been found anywhere else. Certain genes are indeed common to many organisms. The genes participating in glycolysis are shared bacteria, to animals via plants and fungi. Yet it would be very unlikely to see the same genes appear on another planet because even if the organisms would be able to degrade sugar, it would be in another way because an evolutionary history different from ours.
The parasites on land have adapted to their hosts and a rigorous selection has been made. In many cases the natural selection has to select the parasites able to produce proteins very similar to that of their hosts and thus deflecting the biology of the host from where the pathogenicity. Amanite kills fly is extremely dangerous for humans because it possesses enzymes capable of synthesizing a molecule that binds specifically to the RNA polymerase which has protected it from ingestion by some predator potential.
Many viral genes are stolen genes from their hosts and then modified to divert cellular machinery. Thus the parasites adapt to their environment and to the organisms they encounter.
Unfortunately in Alien Covenant the crew comes across a biotechnology specifically designed to destroy man. But as a general rule, there is little chance that an extraterrestrial organism can develop a response against a host whose evolutionary story is dramatic and radically different. .
In addition, the human body is often underestimated in a wrong way, which has a considerable weapon of war which is the antibody. Our body is able to statistically produce an antibody for any molecules (of sufficient size) organic.
