A toilet plume is the invisible to the naked eye, cloud-like dispersal of raw, infectious sewage particles as a result of flushing a toilet. Flush particles rapidly rise out of the bowl and several feet into the air after flushing. Aerosolized droplets can remain suspended in the air for tens of minutes between users, posing an inhalation risk. These invisible particles go on to coat and spread onto surfaces like floors and counters or objects like hand towels, bathmats, or even toothbrushes.
There are people who follow the "10 second rule", i.e. food hits an unclean surface like the floor and they will pick it up and eat it.
Meanwhile, every single person who was born naturally has been shit on at birth. This is a thing that happens. And studies show that excessive cleaning of newborns leads to all sorts of allergies.
So there has to be a balance.
I'm sure a non-zero number of people have gotten ill from toilets flushing. I'm also sure that number is pretty small. And I'm as sure from studies that show that keeping the lid closed still lets particles out that it's going to happen.
I'm of the opinion that this is a very small problem.
But as it happens, I keep my toothbrush at my desk because it's more convenient for me.
So if it bothers you, keep your toothbrush in a cabinet and/or in one of those little cases.