At several points in the movie, they make a point to show that the MUTOs are highly radioactive, being that they consume atomic bombs whole, it makes sense. They do so by showing people in hazmat suits and the like while they are around, in order to protect themselves from the radiation. The scenes at the cocoon being one of them. But at other times, many people are in close proximity to the MUTOs and show no adverse effects to the exposure. Case in point: Ford comes in close contact with the MUTOs on several occasions.
Is it the generally brief exposure that makes this possible, or is it something else?