It's probably an issue with wireless signal interference.
Microwave ovens and most common wifi transmitters share the same frequency band(2.4 GHz).
Changing to a newer router wouldn't help either as chrome cast, as far as I know, only supports 2.4 GHz.
My suggestions for fixes are:
Changing what channel your wifi setup is on. Moving the microwave oven. moving the wifi router. buying a more isolated microwave. using direct connection from the computer to your router (as the chrome cast is still connected this probably won't help). accepting defeat and buy pre-popped popcorn for the next movie night ;-)