Since you've had measles, you know how contagious the virus is. It is airborne, spread by coughing and sneezing. And the initial symptoms are similar to other respiratory illnesses, like a cold or the flu - fever, runny nose, coughing, red eyes, sore throat. According to the CDC, measles is SO contagious that if one person has it, 90% of those around him will get it if not protected. Those are staggering odds of infection.
The only way to protect CMs and impede the spread of the disease is for them to be vaccinated. Why are you so opposed, especially since you've had the disease?