Can I wash these clothes in the washing machine?
Generally, yes, so long as you wash them on the Cold cycle. For most machines, that's less than 80 degrees F (27 degrees Celsius).
Certain high-heat wash cycles (say, a "sanitary" cycle or a cycle for bright whites) could cause the clothes to shut down, and at Warm temperatures (over 80 degrees F) there's a chance you could cause some unsightly wrinkling.
So we strongly recommend you wash them in cold.