First, try telling ehr she can only do this in one or two drawers, the ones she can easily clean up afterward. I don't think she is really doing aything wrong, you haven't really suggested it is tantrum behavior, just playing. Why do you think it is driven by anger? If she were tearing the clothes out and screaming at you, then I would say you have a different problem.
She probably keeps doing it because, she enjoys the taking out AND the cleaning up (even though you don't). Cleaning it up has become part of the play. It sounds like normal 2 year old behavior - my daughter loved to unpack her drawers and fold hand stack her clothes at that age and sort them into bags and other containers, etc. Two year olds are into pretend and mimicing what mom and dad do (like laundry). Set limits. I would just let her play in a couple and restrict the rest. If this is just playing, try reasoning with her - only play in these drawers or no playing at all. I don't know why that wouldn't work. Even empy out a drawer or two and use it for her baby doll clothes and other pretend toys to encourage ehr to have a play space of her own. If it doesn't work, or it's really a big deal to you, here are a couple of suggestions.
Childproof with baby locks on each drawer. Leave one open, and tell her she can play in that one but only if she cleans up afterward. Otherwise, temporarily move the clothes out and turn the dresser against the wall.
Is she napping and just doing this before or is she not napping and playing instead? She is too young to be giving up naps, so I would focus more on helping her get herself to sleep if she is strugging. Consider moving her nap later by 30 minutes or so, she may just not be tired enough. Put a bunch of books n her bed and tell her she can read until she is sleepy. That would solve two problems, sleeping and the mess.
Whatever you do, please make sure she can't pull the dresser over on herself while playing. If it is tall enought that she is pulling on the drawers or climbing it, please secure it to the wall.