3/8th's of an inch is not very thick all things considered - very good chance the shelves will start sagging under the weight of the tubs, making them hard to open & close.

I use 3 different styles of AP's rubbermaid & sterilite racks (1/2" thick) and they work very very well. The lower tubs fit snugly, but not to the point of being a PITA. When dealing with *any* rack that's not going to have support in between each tub, thicker, sturdier material is a benefit!

K~