Okay well.. .for me, this is the age they are getting motivated and independent... and they "mirror" what they see us do and pretend play etc. Its a part of growing up.
BOTH my kids did that too. It didn't bother me. I just slowly taught them to "put away"... and over time they did. OR, if they took things out of their dresser, then I put a basket next to it and had them "pick up" and put their clothes there... since I very well can't expect them to fold the clothes all nicely and put it back at this age.
To me... you can try and bolt the dresser to the flooring or the back wall, so it won't tip over, per safety precautions...since some kids pull out the drawers and use it as a "ladder" to climb and the dresser can tip. Or... you get some "Cubby" type shelving/drawers that he can reach INTO, instead of having to pull out drawers... and then this way, HE can reach his clothing.... and put it back.
I know... having a toddler taking clothes out of his dresser may be messy and irritating... BUT, the sooner they learn to manage this "mess" and then get it out of their system... the better. It is a "phase" you know. It won't last forever.
AND you get some cute coordinated shelving, or those plastic rolling drawer things to store all his toys in too.
I don't know, for me, when my kids did that... well, it didn't bother me. I just made it a part of everyday routine... that we picked stuff up off the floor, and then put it back where it came from. As long as my kids tried their best... I did NOT expect it to be perfect, nor spotless. For soiled clothes... they drop it in the laundry basket.
Just try and make it fun for him to "put away." Then gradually, you will have formed a cute little helpful "habit" in him... and it will engender "teamwork" in him. Main thing being, that they try. Doesn't have to be perfect.
But that's what I do with my kids.
All the best,
Susan