STDs/STIs/Venereal diseases are not massively worse than any other class of disease, however social stigma sees things somewhat elevated and general areas involved means you tend to get specialist treatments for them, much like you get specialist surgeons, ear nose and throat doctors, mental health professionals and so on and so on.
Whether toilets constitute a transmission vector of STIs worth considering as a member of the general public I must confess I don't know. I have read quite a bit of literature for the sexual health profession and saw no real mention of anything there (bathhouses =/= bathrooms), and have otherwise not seen any public service announcements saying bring cleaning supplies to/avoid things if it looks like.
I could see it happening -- a lot of transmission is fluid transmission and of those diseases with symptoms then drippy genitals is a common one. That said the only thing I can think concerning toilet seats is when someone gets pregnant or otherwise tests positive and says they must have got it from a dirty toilet seat, which is a mainly a test to see how gullible someone is or used among the medics as code for "they are a lying idiot".
