I've camped quite a bit on the Black Rock Desert (see my avatar). Yes, you will get dust inside the van, but it isn't the end of the world to vacuum it up when you get home.
When you're not in the van, just keep everything closed and zipped up (I usually leave my penthouse top raised). You might still get some dust leakage through the rear door seals
. Make your bed (or otherwise cover it) so dust doesn't get on your sheets.
When you're with the van and need a breeze (and you're not in the thick of an obvious dust storm), keep just the penthouse windows open -- they're often above much of the basic dust from foot traffic, etc. I keep all the lower windows and doors closed.
Once I forgot to close the penthouse windows before going out walking -- and a dust storm hit while I was far from the van. When I returned, every surface of the interior of the van (bedding too) was covered with a few millimeters of that beige playa dust. Believe it or not, I sometimes bring a small shop-vac for this kind situation.