I think there is a difference between humidity & water injection.
Correct me if I'm wrong - (relative) humidity which is what this topic is talking about is the percentage of water that is in the air below saturation point.
Water injection on the other hand is to decrease the air temperature. A decrease in air temperature causes an increase in air density.
So why does turbine engine not be affected by humidity? From the answers above, I think the answer could be that turbine engine compressors will turn at the speed required to produce the requested "pressure". So if humidity is high (less dense air) the compressors will end up turning faster to produce the same amount pressure required.
Or did I get it all wrong there?
Whereas in a piston engine, the piston just sucks is air and burns it. The less dense the air, the less power produced.
Did I get it wrong again?