You want to know the best part about foam vs cotton gauze?
When dirty cotton gauze flows like ****. I mean seriously, devastating to horsepower bad. I know of an R3 that showed a loss of 30whp from filthy K&N filters....
When foam is dirty, you lose a little filtering efficiency and a couple of horsepower, but it still flows quite well.
This is why it's used in desert racing, not it's filtering ability, not it's robustness vs cotton, not weight, not cost. It keeps flowing even when filthy.
Gently wash as 1olbull said, mild soap, warm water, minimal manual agitation, let the flowing water (inside to outside) do the work. Dry overnight and just dust on aerosol oil spray, done.
My 3 year old PX-600 has NEVER been cleaned, on and off back to back testing was a whopping loss of 1.5whp, from 256 to 257.5, or, 0.5%.