There are many Palestinians, other Arabs, Iranians, Afghans, etc. with blue eyes. Some of them have pretty light skin too.
Ashkenazi Jews are probably descended from Middle Eastern and/or Babylonian Jews, but they were in Europe for over a thousand years, more like 1500 years. That is enough time for the average skin color to change (and eyes and hair too, since skin, eye hair genes are related), for health reasons. Even so, most Ashkenazim have dark hair and many have olive or dark skin (though many are very pale). Blue eyes are common but not the vast majority.
When a single couple has several children, because of natural genetic variation some will be lighter and some will be darker. In far Northern climates, darker skinned people will not get as much Vitamin D, and will sometimes have health problems or be generally sickly as a result, while the light-skinned will be healthier, and thus more likely on average to have children and successfully raise them and keep them alive. A few dozen generations is potentially enough time for the shift toward lighter skin to take place.
Genetic studies also suggest that Ashkenazim were descended in part from converts from Southern Europe, especially Italy, and to a much smaller degree from Western and Eastern Europe. This is not surprising, since Jews have attracted converts wherever they have lived. It may have happened at a somewhat larger scale in Ancient Rome.