I go out of my way to use the old fashion do it yourself carwash ports. I'm usually pretty careful on direct pressure on the top. My 2012 had the normal Mopar top and my 2013 has the premium. I really don't treat them any differently.
I've also used the touchless automatic carwashes on 2012, and I just don't like the dryer pressure on the top - personal preference.
Now, when the soft-top comes down like mine did this week, the doors also go off. So right before I go sans top/doors. I do one good cleaning, waxing, leather protection, and black plastic protection. In this mode, I usually will only wash if absolutely necessary. Here in the desert its mostly just dust - so I don't have to worry much about mud, etc... But, I may end up giving her 1 hand wash after a particularly dusty outing. Otherwise, no bath until top and doors go back on.