Right kids! Pay attention here. There's a reason why the toilet has a lid. USE IT!
This is a matter of personal preference. And not all toilets have lids. Wonder why that is...maybe lids are not for the reason you think.
My daughter kept her lids closed to keep her two cats out of the toilet. In a public restroom, cats and bassets aren't usually going to be a problem, thus, lots of them don't have lids. I like to put the lid down if I want to sit there and talk to someone who is taking a bath. The lid keeps me from forgetting where I am and falling in.
I find paranoia over germs both amusing and bewildering. I understand it's a form of obsessive compulsive disorder. Howie Mandel suffers with the affliction and it makes his life miserable.
Now, I am careful with germs in the kitchen. If you prepare raw meat on the counter, disinfect the counter afterwards. Don't use the same knife you cut meat with to cut up your salad, etc.
Open toilet lids on a clean toilet, not an issue at my house. My preference. No reason for anyone to be ashamed if they prefer their toilet lids open and don't insist they be closed for each flush. Be accurate with biology so you don't create paranoia in yourself and others. Unless someone at your house has a terrible communicable disease that lives in the GI tract, you're probably safe using normal cleaning and handwashing procedures and flushing with the seat up. If it gives you peace of mind to leave it closed, by all means, leave it closed.