I would wash the sheets - to go with the washed top fabrics -
It seems to me that if one buys sheets that are similar in weight and weave to 'quilting fabric' - that there would not be any issues.
Although I have a serious issue with the words 'suitable quilting fabric' - seeing as I come from an era where velvets, denim, silks, cottons, rayons, wools - were used - probably anything and everything except cheesecloth and burlap!
(I'm not saying that all these combinations were 'successful' - just that they were used)