No. I left my top off just about all year last year and no problems. Just make sure and let it dry good before putting the top back on.
"But it does me no injury for my neighbour to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg." - Thomas Jefferson, Notes on the State of Virginia, 1782
Arguing with a truck driver is like wrestling with a pig in mud, eventually you realize the pig enjoys it.
I once had a car get flooded and no matter how much scooping of water the carpet soaked up, the next day, there was more. There was no amount of blowdrying that really took care of it. In the end, I ended up ripping it out. Plus, I was worried that had I kept it, when it eventually dried, I would have to contend with mold spores floating around getting kicked up everytime I stepped on it. Not good!
In your case, I would just rip out all the carpet so I wouldn't have to deal with moisture, mold, fleas, dust, dirt, allergens, mites, etc. that might get kicked up everytime that gets stepped on.
Not sure what year your Jeep is but in my '91, it feels a whole lot better! Yep, the past couple of days of rain here in SoCal leaves the inside of my Jeep wet too but not too much. I really don't have any wires running along the floor board, I just tuck them into the sides and ziptie them. The only wire I know of that cuts across the floor board is that seat belt sensor deal that attaches to the buckle but even I don't use that, I just consciously put on my seatbelt so I don't need that wire.
To get back the insulation I lost from removing the carpet I slathered Herculiner all over the tub and whenever it gets dirty, I just pop open the drain holes and hose it down. In time, the carpet will rot and won't really dry up completely. The seats (at least mine) are covered in that synthetic easy to wipe down fabric out of the factory so I'm not too worried about those. Water just beads down. You can always get neoprene seat covers.
I like to drive my Jeep without the doors and top too and I just don't want it to act like an oversized feather duster collecting all that stuff flying about in the air as I drive right on to the carpeting and accumulating! Yuck!
I'd say, rip out the carpet, Herculiner the tub, and not even have to deal with shampooing anything anymore!
My Girl Likes It Muddy and Dirty!
mine got wet alot last summer, i just let it dry out before i put the top back up. back in april it got so wet it did short out my speakers and i had to replace all 4. be careful not to turn on your radio when it it wet, wait till it dries.
Location: Under a sheet of ice, you know, from Global Warming!
If you have the cover on, your electronics should be ok, as long as there isn't water actually ON them, humidity won't hurt. If you can, get out there and pull the drain plugs under the carpet, it'll let the water out. Keep the cover on, but every time it quits raining, open the sides up, let it air out as much as possible. If the sun ever comes back out, even better! Whatever you do, don't button it back up wet, or it'll smell like wet dog forever!