All the ideas above are good; plastic totes, towels for drying cables etc. If my water hoses are bad (and they usually are in the FL beach sand) I wipe them down as well before dropping in a tote. If there has been an accumulation of leaves, pine needles, debris etc. on my slides I won't bring them in even in the rain. I just pull out my collapsible ladder, grab my extending pole with a brush on the end and brush them all off...doesn't take too long and prevents a potential mess in the trailer.
I think one of the biggest things is mindset along with being prepared. I've camped with some folks that detest the rain and act as if they would melt if out in it. I worked in it, in every shape fashion and form, for decades so I don't mind it. I would be lying if I didn't say it does bother me more than it did when I was younger. Get a raincoat (rainsuit w/pants if it is going to be really bad) and carry it - ponchos are for very limited use. I don't worry about rubber boots; I always wear what would be considered "work" boots so don't worry about the water, dirt, mud etc.; just scrape them off and climb in. All my vehicles have WeatherTech floormats so I can wash them off when I get to where I can.
Another thought; sometimes when you are trying to leave in the rain you will encounter a problem that requires using tools. Rain will ruin your tools. I go ahead and use them, dry them with a towel, drop them either in the back floorboard or bed of the truck then spray them down with WD40 when I get to the next site. By the way, the back of the truck is a great storage place for wet stuff you can't find a place for quickly in the rain.
Edit: I have a BakFlip hard bed cover.