Wow..y'all are on the sanitary kick here as of late..If I even TOLD you of some of the stuff that is unsanitary or unclean, it'd blow your minds.
Also the bacteria you spread on your body. More than likely it is common flora from individual to individual, and even your own. You will never be germ free, you will never be perfectly sterile. It's practically impossible. Also keep in mind, this bacteria must have a route of entry, which means a break in the chain of infection. If it isn't broke, no sickness/ailment/etc.
But honestly I'd be more inclined to think someone would have a bacterial related issue with a food illness or soft drink machine (yes a soft drink machine, they have been noted to carry e-coli in a few studies, drink up kids), than a public restroom.
Also if you're flipping out over a restroom. Think of the queue rails, restraints, seats, turnstiles, park maps, chairs, doors, and everything else you touch. A good bit of that probably isn't any cleaner than that restroom. For example I know we only cleaned queue rails at night or early in the Morning probably every other day or so for my ride. Trains get cleaned everyday no doubt, but a nice hot sweaty day, oh the juices get a flowing.
Moral of the story, theres alot of bacteria and germs out there everywhere, most of you aren't even at the germ capital of the world everyday for employment. It could be alot worse, and most of what you will deal with in the park is common flora, maybe a virus or infectious bacteria here and there, but as long as you don't have breaks in your skin, pick your nose, stick your hand in your mouth, or poke your eyeball repeatedly, I think it would be safe to say you'll be ok.