Apparently the S&G version is adapted from a traditional folksong, where the pertinent verse was originally (and apparently still is):
Have her make me a cambric shirt
Parsley, sage, rosemary and thyme
Without no seam nor fine needle work
And then she’ll be a true love of mine
setting up the shirtmaking as one item in a list of impossible tasks, in the tradition of the fairy-tale heroine who is instructed to meet the prince neither riding nor walking, neither naked or clothed, neither shod nor barefoot, etc. (She meets the conditions by wearing one shoe, dragging one foot on the ground while mostly on the back of a horse or mule, wearing a fishnet, etc.)
Tangent #1: technically, it is possible to make a seamless shirt by either setting up a circular warp or knitting the entire garment.
Tangent #2: the interpretation I’d always heard for the S&G version was that “cambric shirt” was a euphemism for “shroud”, the ultimate minimalism in seamless garments. This ties in with the parallel lyrics about soldiers and warfare. Similarly, “parsley, sage, rosemary, and thyme” were sometimes explained as having been medieval abortifacients; there’s actually a bit of evidence for this-- see_Eve’s Herbs_ by John M. Riddle, which also does a number on Ophelia’s choice in floral arrangements.