Mung beans could make you sick if you're allergic to the mung beans or they are eaten in large quantities.
I've heard that when you eat too many mung beans that they can be toxic whether they are cooked all the way or not.
But when eaten in moderation the mung beans should not make you sick.
But some people can be allergic to the mung beans just like they can be allergic to other certain foods.
If you get a stomach ache, or feel sick after eating mung beans then you could be allergic to them.
Make sure you cook the mung beans all the way before eating them so that any potential bacteria is killed off.
But other than that you should not get sick from eating mung beans.
I eat mung beans about once per week and never have gotten sick from eating the mung beans.