There is a difference of opinion regarding the status of synthetic fabrics with respect to tum'ah and taharah (ritual purity). Presumably, a fabric's status would depend on the majority of its fibers. But any practical questions should be brought with specifics to a halachic authority.
If you are purchasing sheets, we suggest purchasing colored sheets for non-niddah times, since stains on colored surfaces are generally treated leniently, regardless of the fabric. (See our article on stains, "Ketamim", for more details.)
If you have a practical question arising from a stain on a white sheet (as above, stains on colored sheets are generally treated leniently), please contact your local halachic authority or get back to us with details.