Do Microwaves Emit Radiation?

My sister is convinced that microwaves emit radiation.  She won’t even stand in front of one.  She will quickly jump at least 5 feet away or get behind a wall while one is running.  She grabs children and babies and moves them out of the way.  Part of me wants to believe her, but then I think back to my grandparents’ microwave.  This was some 25-ish years ago, in the 80s.  Their microwave must have been one of the very first models, maybe from 1982, or something like that.  It was SO OLD.  It had a strange knob, like a twist-timer, to set the time.  There was one level of intensity, and not even a popcorn button.  I scoured the internet for a similar picture, and found this remarkable one – I think it might be the same exact model as my grandparents!

Microwave from 1982

That makes me so excited.  I don’t know how long they had it, but they used it a lot.  Just for fun, I will post this related picture:

I don't know that guy but I think this was taken in my grandparent's kitchen
I don’t know this guy but I think this was taken in my grandparent’s kitchen

Anyway, I think if microwaves emitted radiation, all 30+ year olds would be mutants from being in the same vicinity as these babies.  As far as I know, I am not a mutant, nor are most other people that weathered the 80’s.  In my opinion, if we are worried about radiation from microwaves, then we should be worried ALL THE TIME (since radiation is directionless, knows no boundaries like walls and doesn’t wane with relatively short distances like 100 miles), and we should probably be more worried about cell phones, since the ratio of microwaves to cell phones is like 4:1 and cell phones are used 100x more frequently.

Although I may sound like it, I am not a nuclear physicist.  Please correct me if you are a scientist and know more than me about this!