For those of you who are ACW re-enactor types, some of the best, most detailed, and most accessible descriptions of pre-modern laundry techniques are to be found in the Civil War Ladies books. Essentially, things had scarcely changed at all between the 1630's and the 1830's.
It wasn't so much that washing caused wear and tear on clothes as that preparing the clothes for washing was so time-consuming.
First, remember that many of the fabrics that they used, especially the wools, are things that we now usually dry-clean because they are difficult to wash. Woolen garments had to be washed separately in cold water to avoid shrinkage and pilling. I will not even address the issue of trying to clean silks, brocades, and other luxury fabrics before the advent of commercial dry-cleaners (though the description of the tasks of a ladies' maid in 19th century etiquette books is very enlightening).
Dyes were not color-fast, and fabrics shrank at different rates. If you read the descriptions of how to wash a "good" dress, the laundress started by removing the trimming and the buttons. Then she separated the lining from the garment itself (picking the seams). If the skirt was full enough that the weight of the wet fabric would cause it to stretch unevenly, she took the skirt off the bodice and took the gores apart at the seams. Then she washed it, dried it, checked to see if the lining and the garment still matched up in size, made any necessary adjustments, and sewed it back together.
This is why shifts, aprons, and pinafores were so important in protecting the main outer garment from soil -- they were much more easily washed, especially the early modern work apron, which was basically just a length of straight cloth with a drawstring run through a casing at the waistline. They were not made with permanent gathers sewed to a band, because those were much more difficult, not just to iron, but to get dry. Similarly, ordinary, everyday, shifts and shirts were not permanently gathered at the neckline and sleeves, but made with casings and drawstrings so the garment could be laid out flat for drying and ironing.
Remember that in early modern laundry (even within my own memory) one of the major problems in winter was getting the clothes dry. Sometimes they could hang around for a week in damp, chilly, weather, with no real way to speed the process up aside from standing and holding the still-dank item next to the stove for a while (which I sometimes did if I needed it for school that day). In the 19th century, most people changed shirts and underwear only once a week.
The major immediate contribution that Grantville can make to European laundry, not of luxury fabrics but of household linens, shirts, and shifts, will be the introduction of the hand-cranked two-roller wringer. Wringing out the wet clothes was one of the hardest tasks on doing laundry. A good wringer with adjustable pressure gets a lot more of the water out with less wear and tear on the hands, and also allows a much shorter drying time.
There should be no technical or material obstacles to bringing this design into production and there were no laundry guilds to hinder its dissemination.
Here are some 19th century machines:
The Patent Model Collection at TMM: Washing Machines
(Thanks to the Wayback Machine.)
This is a slight change of topic for those who think that any Grantville enterprise should have a military application :)
Cleaning the Sword