Corrosion on copper pipes due to insulation (with foam)
I wouldn't bother insulating your incoming cold water pipes.  If your basement is warm, the water will warm up a little passing through it, but the solution to that -- if you need it -- is to let the cold water run for a little until you're see water that hasn't been sitting around in your pipes getting warm.  I say "if you need it" because I generally don't care what temperature my cold water is: drinking water for me comes from a pitcher in my fridge; tap water is used for washing food, mixing with hot water for bathing, or watering plants.

If you're concerned about the condensation from your pipes dripping onto things, I'd be more inclined to get a dehumidifier and run it while you've got this hot, humid weather.