Mold resistant paint?

I know making a rack with wood is not the best idea because of molding problems but what if its painted with mold resistant paint?

You can go with melamine, which has a plastic coating on the outside that would be resistant to moisture, but overtime can degrade. If you go with plywood you will need to seal the wood, which leaves you a variety of options. I have seen people go with something like Thompson's water sealer, which is used to seal wood on decks and the like. Another option is using drylok. It is extremely tough, and water resistant. The only issue I see is that it dries mildly gritty, and over time might scuff the tubs if they are moved in and out a lot. If you have experience with this sort of thing you could do multiple layers of polyurethane. Im not sure about mold resistant paint, but all of these options make the wood water tight and would not allow mold/water to penetrate the wood.

Just remember to let any paint/chemicals fully gas out before you move them inside and put into use.
There is another option, I have bare MDF racks that only show a little wear from sliding the tubs in and out BUT no water damage at all.
Build your racks with lids on the tubs.
It can be a little pain taking the tubs all the way out to take the lid off but when it comes to cleaning it is nice because you don't have to get all in the rack to clean "paint" off of it.