This subject has been brought up numerous times here. One member wrote to a fabric manufacturer (I believe) and they told her that the cardboard that fabric comes on in bolts at the fabric stores is acid free. However, I am not sure what cardboard you are speaking of?
I do know that many members have successfully used various things over the years that were not considered acid free and have had no problems. I have all of mine folded and many people use the ruler fold method and are happy with that. Everyone has opinions about which they prefer and in my opinion there is no right or wrong answer. The main thing is to keep your fabrics out of sunlight as eventually they will fade over time.
As for the specialized boards that you can purchase I personally would not pay for them. We did fine for years and years without them and to me it's just another one of those specialized products that we don't truly need. I'd rather spend it on fabric and threads.