Since you asked about thru-hikers, I will say that a great many thru-hikers and other folks on long trips who have a schedule to meet (that is, a target daily mileage) will just keep walking through the rain. I guess it's a zen thing? I mean, it's not so different than sweating buckets. The east coast has seen humidity around 90% pretty regularly this summer. The air is wet whether it is actively raining or not. Some strategies:
1. Get to know the weather patterns. Often, thunderstorms occur with great regularity every afternoon. Plan on getting up early, putting in your miles during the cool morning hours, and setting up camp before the rain hits. Better to get rained on at camp than rained on while walking.
2. Take advantage of mid-day sun. Walking in mid-day heat sucks anyway, so if the sun comes out and the clouds burn off, take a long break and spread out all of your gear to dry. A couple hours in direct sun should take care of tent, trail runners, clothes, etc.
3. Make sure your vital insulation pieces are protected at all times. A friend of mine refers to the dry bag that holds his sleeping bag, puffy, and sleep clothes as the "inner sanctum" of his pack. Double wrap that stuff! I like down, and use it even when it rains, taking care to keep it in a plastic bag inside a dry bag.
4. Pack covers are pretty worthless. Pack liners (e.g. a trash compactor bag) work better. Pack covers will keep the pack itself from absorbing some water, but the shoulder and hipbelt pads act like sponges anyway, and I find that water always manages to run down inside the pack cover during heavy rain.
5. Even in the summer, bring full rain gear. A lot of people here will disagree with me, but being stuck in an all-day deluge without insulation can suck. Up on ridges and balds, the wind can pick up and easily drop temps down into the 40s and 50s in mid-summer, and if you're sopping wet you can be facing hypothermia conditions. Some people are happy with ponchos and skirts/chaps; I find that most of the time I really need a full jacket and pants for the extra warmth.
6. Sleep clothes! I'd be miserable without a set of dry clothes to change into. In the summer, it's just a tank top and shorts, or a light dress, plus a warm hoody on top. Some camp shoes to get your feet dried out is a good idea, too, for the health of your feet.
7. As has been established time and again, waterproof-breathable shoes are never truly waterproof (or breathable). The only thing that will keep your feet dry is something like a full rubber muck boot. Great for farm work, terrible for hiking. Your feet will get wet–fact of the backcountry. A lot of people deal by wearing quick-drying shoes that hold less water: either trail runners with lots of mesh or sandals designed for water (i.e. Chacos or Tevas).
This is how I've gotten through this record-setting rain year, but I'm sure there's more I'm forgetting.