I have heard of WiFi slowing down when a microwave is running.

Also when a phone is in a microwave, the RF noise is also attenuated, so that helps a little (amplifier noise is unaffected).

My wireless headphones get an unbearable amount of pops and cracks when I'm wearing them close to my (running) microwave. But since I wear them virtually always, I am in effect virtually never next to my microwave when it's on :)

Yeah the shielding is to not cook your eyeballs if you observe the food, and to not cook anything else outside of the chamber, including e.g. your phone's wifi receiver.