The proper term to use when referring to someone of Jewish ancestry or a member of the Jewish faith is “Jewish,” although “Jew” is technically correct. However, “Jew” has become laden with negative connotations which have led most people to conclude that it should not be utilized in polite conversation, for fear of being viewed as an insult. The plural form, “Jews,” along with “Jewry” to refer collectively to Jewish people around the world, is appropriate for use in most regions, although individual people may express personal preferences which should be respected.
Unfortunately, antisemitic attitudes about Jewish people have persisted worldwide for centuries. As a result, these attitudes have shifted the way in which people view the word “Jew.” Technically, however, it is just a proper noun used to describe a person of this ancestry or faith without awkward circumlocutions.
The issue is that “Jew” is often used as a pejorative. Antisemitic rhetoric refers to “dirty Jews” and uses “Jew” as though it is an insult, rather than an adjective, and as a result, it sounds jarring to hear someone referred to as “a Jew,” rather than “Jewish.” Furthermore, the word has also historically been used to describe being cheated out of something, as in “I got Jewed on that deal,” referencing a widely-held stereotype that Jews are greedy swindlers.
In most cases, words which describe racial or national origin can be used both as nouns and adjectives. For example, one could say “she is Turkish,” or “I am drinking a Turkish coffee,” and both would be appropriate. “Jew” and “Jewish” are the rare exception to this rule. “Jew” should never be used as an adjective, and its acceptability as a noun is debatable. Using these words appropriately is not just a matter of being politically correct: it's a recognition that there are complex linguistic undercurrents involved.
Adjectival uses of “Jew” like “she's a Jew lawyer” sound jarring to the ear in a way that “she's a Jewish lawyer” does not, thanks to cultural perceptions about the word “Jew.” The history of the use of “Jew” as an epithet, rather than a simple noun or adjective, has made it a loaded term to use. While describing someone as “a Jew” may be accurate in the literal sense, in that someone of the Jewish faith or descent is indeed a Jew, it is generally frowned upon, and should be avoided, if possible.