More than the stains, it is the smell that can be troublesome.

I am using a fairly pungent dish detergent, which keeps the bugs away, but every plastic vessel would readily absorb the scent, and I stopped wanting to store or eat anything in them.

Now, I avoid immersing any plastics in the sink until I'm ready to rinse immediately, so it's an extra step of labor, for the privilege of plastics.