People's personality is 30% born to be and 70% affected by the living environment. The eye color is born to be which is determined by the genetic genes. They may have the relation from the inner body mechanism. However your personality is more or less determined by your inner mysterious body mechanism. The environment you live is so important which will change it in the later time.
I have to tell you that there is no reasonable relationship between them.
As we know the eye color is genetic while the personality is mainly determined by the environment and acquired experiences. Only if you have a stereotype in your mind when deal with people, there is no difference in dealing with people with different eye colors. That's some like the skin color and personality, we have to hold a fair attitude to judge people with different colors, right?
No, it isn't. Eye color can affect your outlook indeed but not personality. Personality can be decided by education and environment. Personality can be changed by many factors, however, eye color cannot be changed naturally. But not all ways cannot help it. You can wear color contact lenses to enhance your look.