The reason why I thought about harmful mutations in this context is because this strain of yeast has some kind of property that activates the immune system, otherwise the whole concept wouldn't work.

That's not something regular yeast does, so for regular yeast to evolve something like that, that's a major step in evolution that doesn't happen quickly.

But modifying the immune system activating payload is much less difficult.

Due to the Hoskins effect, it's possible that an immune system trained for a "somewhat wrong" pathogen can perform worse than one that hasn't seen that kind of pathogen at all before. So if the payload of the yeast mutates, it can "mistrain" the immune system so that it then performs worse on the real-life pathogen.