In the USA, the FDA requires testing of microwavable containers. According to this site:
Microwave-safe containers go through stringent FDA testing to ensure that, at temperatures reached in the microwave oven, the amount of chemicals that leach out of the plastic is no more than 100 to 1,000 times less than the amount shown to harm lab animals.
If they say "microwave safe" they are supposed to have met the above standard.
They go on to further state that the descrtiptor PET (polyethylene terephthalate), is not enough information to determine safety in the microwave, as some PET containers/material are/is microwave safe, while others are not.
You can also look at the container itself, as you can see here, there are several symbols that indicate whether a container is safe in the microwave.
But...there is some debate about the actual meaning of "microwave safe"...does it mean non-toxic? ....does simply mean the container will not melt and potentially burn the user?
Personally, I would avoid melting or shape changing containers, as that might mean a higher risk. In the end, you will have to be the judge for you and your family. I know it's less convenient, but, if you are really concerned, you could certainly remove the food from the storage container and into something like ceramic or glass to reheat.