Well, it depends. Natural fibers are not stay dry. While you can find natural fiber diapers with a stay dry layer, be aware that the stay dry portion is a synthetic.
Natural fiber diapers I can think of with a stay dry layer:
Swaddlebees Simplex AIO, but it might only come in snaps.
Grovia AI2 with the stay-dry inserts. The aplix on these is quite good.