Jewish people are interesting for their part of both an ethnicity and a religion. The Jews don't preach or actively try to convert people, the religion has largely remained practiced by three main groups and a few smaller ones. The three main ones that are Caucasian looking as you would say are the Ashkenazi, Sephardi, and Mizrahi. They make up almost all of the Jewish population. Ashkenazis are the Jews most people are familiar with as they make up 70-85% of the Jewish population. They resided in Germany, Poland, and other Eastern and Central European nations. Given the time they had resided in Europe it is understandable that they would bear a lot of resemblance. Einstein, Freud, Natalie Portman, and Anne Frank are Askenazi. The Sephardic Jews used to reside in Spain(Sefarad in Hebrew) until the Inquisitions of Spain and Portugal. Again they spent time among the populace of Iberia. Maimonedes was a Sephardic Jew. The Mizrahi are still Caucasian but more Middle Eastern as they resided in Babylon after the destruction of the First Temple. They are still Caucasian as Middle Easterners are Caucasian. Paula Abdul is Mizrahi. I have Jewish relatives well versed in the history if that counts as a source. I could look one up now though. If you have any questions, feel free. Edit: I hope this will do, I know Wikipedia is not the best source but it has a decent summary of ethnic divisions: http://en.wikipedia.org/wiki/Jewish_ethnic_divisions

A quick google of The Jewish Diaspora returns a fantastic Wiki article.

A 2013 study of Ashkenazi mitochondrial DNA by Costa et al, reached the conclusion that the four major female founders and most of the minor female founders had ancestry in prehistoric Europe, rather than the Near East or Caucasus. According to the study these findings 'point to a significant role for the conversion of women in the formation of Ashkenazi communities.

Remember that for centuries, Jewish history is a series of expulsion, trade, and migration. While that pattern spread across the globe for 3,000 years, the majority of that migration happened in Europe. So over time those people lived and reproduced with other Europeans and various groups travelling/conquering thereabout.

Nevertheless, Ashkenazic and Sephardic Jews have roughly 30 percent European ancestry, with most of the rest from the Middle East.

So, to go any further I think this question is better suited to /r/askscience or /r/biology because it is beyond the scope of historians to answer why skin appears "White" despite most genetic markers hailing from the Middle East.