How to keep dust and cat hair off cast iron pans?
First off, cleaning isn't necessarily bad for seasoning.  "Soap removes seasoning" is largely a myth; Serious Eats discusses this at length.  The seasoning is actually a polymer chemically bonded to the iron, not just something coating the outside that will easily wash off, so anything that isn't able to remove the iron shouldn't remove it.  Certainly a light wipe with a wet or soapy cloth is perfectly fine.

Second, a few options you might consider:


If you're hanging it on the wall, hang it so the main part of the pan faces the wall.  This will mean less stuff gets on it (and more gets on the bottom, which is irrelevant).
If you crochet or knit, or know someone who does, make a cast iron pan cover.  I know a friend who did this.  You can make it out of a relatively heat-resistant yarn, so that it isn't damaged by the pan being warm.  You might also be able to reuse an old sweater, as long as you confirm the fabric is something that can stand up to the heat (100% cotton is probably best since it's hard to say what different polyesters will do).
While the pan cools from your seasoning, keep it in the oven, or turn it upside down.  That way it can be cooler before you cover it.
Buy enamelware.  Maybe cast iron isn't the best idea in a long-hair cat household.
Before using the pan, heat it up a lot (20 minutes or so in the oven or over high heat).  Then brush off whatever is on it (carefully).  This will remove the cat hair effectively without risking any damage to the seasoning.