Does showing more skin at the gym equate to spreding more germs?

No. there are certain routes germs can take getting from one person to another. sweat is not such a route.

But if you go to gym while having a cold then you will spread more germs, not just cold germs, but whatever germs are in you will be expelled through your mouth and nose when you sneeze and they might then find a new home in another visitor to the gym. Likewise if you pull your pants down and defecate on the floor of the gym you will be spreading germs for others to catch. Peeing is not so bad. Urine will kill most germs.

Open wounds are also openings that germs can exit you and enter others through. Unbroken skin however is quite effective at stopping germs trying to get in. Herpes is one of the very few bacteria that can get in that way.

It's getting hysterical and very unhealthy.

I don't know where this fear of skin comes from. I see these pathological fears spreading like a fire in the steppe. It is very alarming how we impose an unhealthy relation to the body for our younger generations. 

I think it comes from the über-moral brigade that thinks skin means "Slut who will have sex with anyone".

Most of the women I see at the gym should probably not show ANY skin.

its possible