Specifically, all the recommendations I have seen are that you should not microweave or put in the dishwasher plastic containers. That's for food, so you can see where the leaching concerns would be.
But I wonder for this if part of it is that it has such close proximity to a lot of your face.
The walls are but the walls don't directly touch anything in there to directly leach. Also, a lot of dishwashers have metal tubs, and this is probably a big reason why.
