I've stored grease fleeces out in the shed in sealed plastic bags for years (up to 15 years!) and, when the bag was opened and the was fleece laid out on the skirting table for an airing, it's been as nice as if it were fresh off the sheep.
Moths were a problem with 2 fleeces and both had holes torn in the bags. Wasps were a problem in one fleece which was not stored in sealed plastic bags, just in a cardboard box. It was this one fleece which led me to sealing all grease fleeces in plastic bags.
The thing with plastic bins is that they have air holes. Small rodents, moths and bees (wasps, hornets, etc) can get in there. Small rodents can and will chew through cloth but it seems that they will not chew on plastic.
Yes, there is a school of thought that says storing fleeces in plastic is not a good thing and will ruin the fleece. My experience is that it does not but my experience with grease fleece storage in sealed plastic bags under non-climate controlled conditions is limited to grease fleeces from sheep breeds from my flock. It is quite possible that fleeces from other breeds with higher or lower grease content stored the same way in a different climate may react differently.