Humidity can damage more than your pantry. Mildew can damage just about everything (I have too much experience with this)
, and some molds may even be a moderate health hazard.
Tackling dampness and mildew in the basement should be a high priority. Bonanacrom is right, but if that's too big a project, at least buy a couple dehumidifiers.
Do some research, use them properly, and you might be amazed at how pleasant a space your basement can become.
Bottom line: Rather than approaching this as "protecting your food from moisture", approach it as a full-on attack at preventing the moisture to begin with.