It sounds like lubricant haze, since it's even. Fungus is never an even haze. Just unscrew the cells from the shutter and clean them.
Storing lenses in a warm environment can cause this, so can storing lenses wrapped in a synthetic fabric, or a camera bag - plasticisers can be miserable to get off glass surfaces.
Lubricant haze results when the lube in the shutter starts to creep and break down. It can also be the result of using the wrong lubricants in a half a$$ed CLA.