A parabolic solar cooker is nothing dangerous, at least to my opinion it is far less dangerous than the use of open fire used for cooking by burning wood, kerosene or gas.
Most people are afraid of the reflections of the sunlight in the mirror hitting the eyes accidentally while handling with the solar cooker. In fact it is not nice if sunlight suddenly hits your eyes, but it is not more dangerous than the sunlight flickering through the leaves of a tree when we look up into the sky. The eyes are capable to be exposed to the full sunlight for a short moment without being damaged, otherwise most people on the would should be already blind! (click here for more). And:
The light reflected by the cooker is not more dangerous than the direct sunlight
as long as your head is not inside the mirror of the AMSI-cooker! WHY? Because the rays of sunlight are concentrated to the focus and the closer they come to the focal area the higher is the light and energy concentration, but if they don't hit the cooking pot or anything else in the focal area, then the light beams continue their straight way and will be diffused again. So the light intensity increases on the way from the parabolic mirror surface to the focal area and it decreases again after passing the focal area. This makes parabolic solar cookers with a focal area outside of the mirror much more dangerous than the AMSI-cooker, because people and burn able things are more probable to come into the area of light and heat concentration. After a travel from the mirror to the focus and the same distance again the light concentration is the same as direct sunlight and after a longer distance it is even less than that. That means that the light intensity of reflections from the AMSI-cooker is less than direkt sunlight and will not lead to any permantent eye damage. But anyway:
Don't put your head inside the cooker (close to the focal area)
But usually nobody does, because it is very hot there as well, and you would not put your head into open fire, won't you? Maybe small children may come close to the focal area with their head, when cooking in the morning or evening hours when the mirror has to be set nearly vertical to catch the light. Small children like and tend as well to stare into strong light and they might have a long reaction time to something that hurts. Therefore:
But the distance of your arm length is enough, so no problem cooking with a baby on the back. So the light coming from the cooker is not more dangerous than sunlight. But staring into bright light for a long time might of cause damage your eyes! This happens for example often when people are watching an eclipse of the sun without proper eye protection. The light coming from the mostly covered sun is much less than the full sunlight, but it can already cause injuries, when people stare in the light for a long time. Therefore:
Wear sun goggles if you have to look into reflections for a long time
For the usual cooking there is no need to do this, as the pot should be (painted) black and most light is hitting the pot and converted to heat without much reflections. During the best cooking hours around noon the mirror is about horizontal and most light hits the pot from the bottom, but in the morning and evening hours when the cooker has to set up upright to catch the sunlight the upper half of the mirror is above the pot and sends light from top into the pot. If the food to cook has a bright colour (like unroasted coffee beans) the food might shine very bright, causing a little pain at the beginning when you start looking onto it. If you need to look into the bright reflecting food for a long time you should wear sun glasses as well! Therefore:
Wear sun goggles if you have to look for a long time onto something bright placed in the focal area
This especially important if you place a white sheet of paper into the focal area to test if the cooker is good made and right adjusted. You have to look onto the paper until it burns, not to burn your fingers. Keep in mind that it is about 200°C in the focal area even if you can't see any fire! So don't touch the metal supports in the cooking area with bare hands. Therefore:
Use gloves or a thick dry cloth around your fingers if you touch hot metal parts in the focal area
And because hot parts may accidentally fall down and it is easier to place the cooker in position:
Place the cooker on clean and level ground without dry grass or other which may burn easy
And here is the last safety rule to protect the cooker and avoid any reflections when the cooker is not used and to protect the cooker from rain, dust and playing children:
and fix it in that position, so it looks like an umbrella. The cooker is also very stable to wind action in this position.