You'll be fine, you just may have to replace them eventually once the sun weakens the plastic or a rodent chews through the side to get to the goods.
Many people use a galvanized trash can due to those two concerns - we did too, and it was fine for years but found out that after time if you don't inspect the lids before rain season, they can potentially leak water where the handle attaches, then get all your feed wet inside and rot it. I store my feed in a dry cabinet under the new coop now, but learning from that experience I try to only buy a max of 3 bags of feed so things don't get stale, as a bag lasts us about 2-3wks.
Good luck