Yes, Swimmer, I used 1/4 ply for everything. But it is not ordinary construction grade stuff -- this is baltic birch ply. A little more expensive, no splinters, looks good on both sides and the edges. Reinforce where needed. Support it as needed.
And note that the shelves, while long, are only a foot wide. So they don't sag in that dimension. If you need shelves that are two feet by two fee, for example, I doubt that quarter inch would be stout enough.
And the reason I use quarter inch has little to do with weight -- it has to do with bulk. Thick shelves and supports (like the one inch MDF clunkers that came stock with the trailer) waste a lot of cubic inches. Storage is at a premium, of course.