I've been mixing them and never gave it any thought. However I prewash everything so maybe that makes a difference. I've not noticed having tension issues moving between them on the LA.
The only problem I've had is that I have experienced more bleeding with batiks than the other fabrics. And that is after prewashing too. At least most of the batiks I've used are multi-color to start with so the bleeding isn't that noticeable to anyone but me.