Deet can indeed damage petroleum-based fabrics, which is a pretty wide swath of material. So, no, you don’t want to be dousing your gear with deet. It’s strictly for use on skin (or on a cotton T-shirt, if you can put up with some staining).
You can, however, treat clothing or other materials with permethrin-based insect repellents. Permethrin is a synthetic insecticide that’s similar to pyrethrum, which is extracted from chrysanthemum flowers. It actually kills insects or inhibits their ability to buzz around by screwing with their nervous system. It’s not harmful to humans if used properly (i.e., treated clothing must be dried completely before wearing) and won’t damage fabrics.
Permethrin-based products come in spray-on or wash-in varieties. The spray-on is of course easier to use聴you just mist a garment with it and then let it dry. A company called Travel Medicine makes both types under the Fite Bite label. An eight-ounce bottle of the wash-in stuff, enough to treat four sets of clothing, costs $25. A bottle of the spray-on is $8. The spray stuff is also available under the Repel Permanone brand.
One nice thing about permethrin is that it stays active for weeks, even if you wash the clothes several times. So it’s really pretty economical to use.
Happy bug fighting!