Some fabrics are lighter weight and still considered suitable for quilting. Often they are called "lawn" in the description but not always. Batiks are typically a wonderfully light tight weave for example.
Follow your gut instincts on whether or not to use your time on these. I would suggest that you change your needle to a lighter weight (so, if you typically use 12 try a 10) and/or one that is listed as a sharp.
I always suggest changing needles with every project anyway. Needles are much cheaper than your time and it's been my experience that people don't change their needles often enough. Hint: If you ever hear your machine going "pooka pooka pooka" while you stitch, your needle is past dull!