I store my panfish soft plastics in trays, along with jig heads etc... They do just fine
However with bass soft plastics, I recommend leaving them in the original bag, and finding a way to organize them. I tried storing different color flukes and rage craws in 5$ trays from Walmart and it completely ruined the trays, within a couple months.
The baits themselves were fine but the trays, not so much.
So I learned the hard way that it's just best to leave them in the bag.