Can one bring shelter infections/illnesses home to own cats?

let's say someone visits a shelter and picks/pets its cats, should they wash their clothes in order to prevent shelter illnesses from getting to their own cat?

or 

does that bacteria die on its own in 2 hours? 

I would say it entirely depends on what illness you are talking about.  I would definitely wash my hands thoroughly.  For SOME diseases, I would think the bacteria/viruses could linger, but don't think any cats that sick would be out for the public to see.  They shouldn't be, anyway. 

Bluecapps said:

 
let's say someone visits a shelter and picks/pets its cats, should they wash their clothes in order to prevent shelter illnesses from getting to their own cat?

or 

does that bacteria die on its own in 2 hours? 

Click to expand...

In theory, yes 100% you could bring something home, but in practice it really depends on who you've touched, how you touched them and how many you touched.  Viruses which are the vast majority of URI related illnesses can last a long time, and parasites like giargia and coccidia also can live outside the host. 

But if you just were visiting a shelter and just touched them with your hands, then i would wash my hands.  If you held them on your chest I would remove your shirt and wash it at home.  if you work there and are regularly exposed (especially to snot and feces) I would be doing more.