You ever seen an airtight toilet lid? That ain't doing shit against aerosolized fecal particulates. Don't worry though, no one's gets sick just breathing the air in a bathroom, most public toilets in America don't even have lids. If "fecal mist" was an actual health risk, the science would be well in by now, the patterns would be unavoidable and ubiquitous. Maybe if you lick the walls where the bathroom air condensates you might get sick, but most people are reasonable enough not to do that just by instinct.

Mythbusters tested this. With the lid open or closed, poop particles were detectable in every room of a house after a flush. The lid does nothing.