The fibers of rayon will weaken & split or fray if the garment is washed a lot. This is why they put “dry clean only” on rayon. There is minimal shrinkage in rayon.
Some manufacturers put “dry clean only” on their product, so they get professionally pressed and look just as nice as the day you bought it in the store… This is also the case with rayon.
However, Rayon can be washed. Cold Water only, tumble dry (lowest heat) for about 5 minutes & hang to dry. Sometimes I spray the garment with spray starch so it doesn’t feel so limp after it drys. You may/may not need to touch up with an iron.
I sometimes wash many rayon items and then take to the cleaners for “press only”
Just my two cents from someone who used to work in a dry cleaners.
PS If you have a lining, see what that is made of. Most are polyester and can be washed.