Being that I am Jewish, a levite, speak hebrew, went to Rabbinical seminary for two years in Jerusalem, and have seen every episode of Star Trek TOS, TNG, Voyager, Deep Space Nine, and mostEnterprise all in order, as well as all of deep space ninethe movies, I may be uniquely qualified amongst members of the site to answer the question.
From NimoysNimoy's own mouth, "As a Jew from Catholic Boston, I understood what it was like to feel alienated, apart from the mainstream" So the isolation that he felt as Jew in a gentile world in which Jews have values and a culture alien to the rest of society, aided him in the same isolation a loan Vulcan would have among humans. He also said, "There were a number of values in 'Star Trek' that I felt very comfortable with as a Jew," he added. "The futuristic society is a meritocracy that values education, social justice and tikkun olam, repairing the world. That's exactly what we were out there doing on the Starship Enterprise: trying to heal the universe." Tikun Olam which is essentially doing things to help society in general which was a uniquely Jewish concept he learned growing up as a Jew. http://www.jewishjournal.com/arts/article/bimah_me_up_scotty_20031205/
There are so many Jewish themes such as the holocaust less than twenty five years after it ended, being the children of Jewish immigrants from those countries, and having to dress up in nazi garb. In terms of social action episodes and a Jewish perspective on how to handle things clearly Kirk and SpocksSpock's characters ellucidateelucidate this as I referenced above in their own words.
Also I forgot to add that the Vulcan high priestess'spriestess garb was similar to the Jewish High priest's garb. And SpocksSpock's white gown after he was reintegrated in the third movie was similar to a "kitel" which is a white gown Jewish men wear on the high holidays. Again I'd put citations to show photos but I can only put two links as my rating is too low as a first time poster.
The actors who play WorfsWorf's parents are very famous Jewish/YiddushYiddish theatre actors "Theodore Bikel and Georgia Brown" Bikel played in "Fiddler on the roof" the main character TeveyahTevye (had to remove citation link). With a last name of Rozhenko, the yiddushyiddish accents, choice of actors, RozchenkoRozhenko is from Belarus a Jewish area, Mr. RozchenkoRozhenko is a doctor, and the manner of their characters in the episode, clearly Worf was raised by Jews.
In addition to Nimoy and Shatner being Jewish, Walter Koenig(Chekov) is Jewish as well as Mark Lenard(Sarek SpocksSpock's father). (had to remove citation link)
In Judaism you are Jewish if your mother is Jewish, plain and simple. You cannot convert away from Judaism. The reference above to charem has nothing to do with being Jewish it only has to do with your status in the Jewish community. It's the same as being cutoffcut off, censured, or shunned(much like excommunicated in catholicism). You're still a full Jew with all of the obligations of a Jew. (had to remove citation link)