Most plastic dishes are microwave safe so you can safely microwave plastic dishes.
If the plastic dish or cup, plate etc is microwave safe it will usually say on the bottom of the plastic dish that it's microwave safe.
Plastic cups or plastic plates though that are considered single use or disposable plastic plates and disposable plastic cups are usually not microwave safe and can melt.
But other plastic bowls, plastic plates, plastic cups etc that are not disposable and are meant to be used more than once are usually safe in the microwave.
I've microwaved food in plastic bowls, on plastic plates and even microwaved plastic cups and never have I had one melt.