I have my fabrics in one of those cheap-o white plastic shelves and the stacks do topple over because the shelves are spaced too far apart. The vertical dowels are a great idea.!
My 2-yds. & over fabric is folded and stored in a big plastic tub. I did have a traditional bookshelf kinda like yours but one shelf fell out of its slots because it got too heavy. Who knew fat quarters could weigh so much!?!