I would probably personally use the microfleece only because it feels nicer and some bubs react to suedecloth.
I've never heard that about the microfleece and cotton not being aboe to be washed together, so I'd probably give the towels a run. I'd only use a couple of layers as otherwise it would be too bulky to sew.
Towels don't go crunchy without fabric softener, they go crunchy drying without movement, so as long as it's line dried it should be fine.