Everything is washable in one way or another.
Cotton/linen or cotton dish towels, bread cloths, and napkins can be machine washed and dried. Use whatever temperature you normally use for your laundry; even hot is fine. If they are shaken a bit when moved from the washer to the dryer and taken out of the dryer soon after it stops they won’t need ironing, but if you want to press any of these items a hot steam iron works best.
Scarves and shawls of any fiber content are best washed by hand. Wool or silk scarves should be washed in cool water with a mild detergent like blue Dawn dishwashing liquid and can be hung or laid flat to dry.