The answer is no. Most diseases, in order to spread, have to get inside the body. When you sit on a toilet seat, your touching it with your skin, whose whole purpose is to keep you in and everything else out. It’s pretty good at that job, too.
Even if a toilet seat is covered in filth (which, sadly, it often is), it can’t actually get into your body. You could get it on your hands, which then convey it to your mouth, but that applies to everything you touch in the bathroom. So wash your hands when you use the bathroom. (If nothing else, just because you happen to be where a sink is.)
You can’t even get herpes from a toilet seat; the virus is just too fragile. There have been exactly zero reported cases of toilet-seat-mediated herpes transmission.
There are a very few rare skin diseases that could be transmitted, but that’s just theoretical; I’m not aware of a single case of it actually happening.
Other people’s urine is kind of gross, but it’s also usually sterile. Even when it’s not (such as a bladder infection), it can’t infect you unless it gets inside you somehow, which is vastly more likely to happen via your hands than your butt muscles. (Your anus is a potential route, but it’s not actually in contact with the toilet seat, and it’s also pretty good at keeping stuff out.)
So if toilet seat covers are not popular for their protective qualities, why does our society still use them? Put simply, the ick factor. That’s it. Because a few people think that a thin film of tissue paper will somehow ward off disease, they choose to spend the money, and waste the natural resources to keep propagating the myth. Here on PLU, toilets are cleaned daily and in some high use buildings like the University Center, they’re cleaned twice! But also on PLU, cases of toilet seat covers are purchased at $39 a pop, about 24 cases a month.
For what? Toilet seat covers do not protect your bum even when toilets are dirty, and at PLU they are cleaned daily. This is an expensive and wasteful product designed to clog toilets, make messes and fool those people in society who are scared of coodies. The only reason they aren’t being yanked from PLU bathrooms everywhere is the fear that people will just start using toilet paper to drape the seat instead. This is a bigger problem than just toilet seats. There needs to be an education campaign to show how to be safe, but how to do so with sanity.