Plastic coops are no guarantee against red mite!, despite some sellers claiming they are! , plastic just makes it a whole lot easier to clean them out should you get them!.
With wooden coops as mentioned, there are lots of nooks and crannies for them to hide in, especially under felt roofs!, which usually get over looked if you are unfortunate enough to get an infestation, the felt would have to be stripped off and replaced, as well as treating the wood! .