Using the spore drive still when they said that kills lifeforms earlier on.
But it doesn't. That was all a mistake, a poor understanding of what the "May" being was trying to convey. Culber's ghost was killing lifeforms, and "May" initially mistakenly associated this with "Captain Stamets" and the ship he was flying through the network, because Culber's ghost was following that ship. The heroes dealt with the problem. And in any case, it wasn't something they brought upon the network: Culber's ghost was using a native lifeform as May repellent, and its poison thus wasn't a new element to the network, but something belonging to it in the first place.
The only reason Starfleet considered stopping spore-jumping was because of the combination of it no longer being needed for defeating the Klingons, it being painful to Stamets, it having been illegal to make Stamets a compatible pilot, and it being a poorly understood force affecting the entire multiverse. But none of that really mattered: the heroes ignored their superiors' "recommendation" and suggested that Pike make use of the drive for studying a distant mystery that posed no immediate threat to the Federation (because it was so distant, doh!).
Timo Saloniemi