Depends on how it's used
Jew or Jewish is a religion. Hebrew is the nationality or Isrealie.
Whether it is offensive or not depends on how it is used.
"Those who do not learn from history and condemned to relive it".
"There are those who will debate the necessity of wilderness, I will not, either you know it in your bones or you are very very old". Aldo Leopold - Sand County Almanac
You know what's sad? Enter the term "Jew" in Google and you get this from Google.
Google: An explanation of our search resultsIf you recently used Google to search for the word “Jew,” you may have seen results that were very disturbing. We assure you that the views expressed by the sites in your results are not in any way endorsed by Google. We’d like to explain why you’re seeing these results when you conduct this search.
A site’s ranking in Google’s search results relies heavily on computer algorithms using thousands of factors to calculate a page’s relevance to a given query. Sometimes subtleties of language cause anomalies to appear that cannot be predicted. A search for “Jew” brings up one such unexpected result.
If you use Google to search for “Judaism,” “Jewish” or “Jewish people,” the results are informative and relevant. So why is a search for “Jew” different? One reason is that the word “Jew” is often used in an anti-Semitic context. Jewish organizations are more likely to use the word “Jewish” when talking about members of their faith. The word has become somewhat charged linguistically, as noted on websites devoted to Jewish topics such as these:
Someone searching for information on Jewish people would be more likely to enter terms like “Judaism,” “Jewish people,” or “Jews” than the single word “Jew” In fact, prior to this incident, the word “Jew” only appeared about once in every 10 million search queries. Now it’s likely that the great majority of searches on Google for “Jew” are by people who have heard about this issue and want to see the results for themselves.
The beliefs and preferences of those who work at Google, as well as the opinions of the general public, do not determine or impact our search results. Individual citizens and public interest groups do periodically urge us to remove particular links or otherwise adjust search results. Although Google reserves the right to address such requests individually, Google views the comprehensiveness of our search results as an extremely important priority. Accordingly, we do not remove a page from our search results simply because its content is unpopular or because we receive complaints concerning it. We will, however, remove pages from our results if we believe the page (or its site) violates our Webmaster Guidelines, if we believe we are required to do so by law, or at the request of the webmaster who is responsible for the page.
We apologize for the upsetting nature of the experience you had using Google and appreciate your taking the time to inform us about it.
The Google Team
P.S. You may be interested in some additional information the Anti-Defamation League has posted about this issue at Google Search Ranking of Hate Sites Not Intentional. In addition, we call your attention to Google’s search results on this topic.
Obviously some people (actually far too many people) use "Jew" as a pejoritive, so I think it's understandable if Jewish people are a little extra on guard when someone uses the term "Jew".
However, with mother's warning in the back of my mind and X Factor's post, I'll probably just stick to "Jewish people."
"It ain't what they call you, it's what you answer to." - W. C. Fields