This seems like something that should be true, but I think I remember seeing a Mythbusters episode where they decided it didn’t make a difference. That show was more about entertainment than science, so I wondered if there was a more rigorous study done? I’ve definitely seen splashes of water(?) come out from flushes so that alone seems to argue for closing lids.
There have been zero deaths reported from a few micro droplets of toilet water as far as I know. Plus there are way more nasty things people already do yet don’t care such as not cleaning their phones on the daily, eating without washing hands, letting their pets such as dogs lick their face and lips, etc.