I personally don't find it offensive and haven't met many Jews that do find it offensive but I live in Australia so I can't really say for followers of Judaism that live in America (nor can I say for all those that live in Australia). Heres what I found online though:
"It came from the Hebrew word Yehudi, which is derived from the name Judah, one of the patriarch Jacob’s sons. The word Judaism stems directly from Judah-ism, the religion of the Yehudim. But for almost as long as there has been Judaism, there have been stereotypes about Jews. By the time the Christian heroes of Shakespeare’s “Merchant of Venice” referred to Shylock repeatedly as “the Jew,” there was no question that the word was a slur, not just a noun noting Shylock’s religion."
But perhaps the most prominent reason for offence at the word comes from WWII and the persecution of those of Jewish faith. Jews of Nazi-occupied countries were forced to wear yellow Star of David badges that simply read “Jude”: German for Jew. So, for many of Jewish descent, this was their Grandparents as it was mine. For some, the word Jew is used to describe part of their identity, but for others, it is a reminder of the times when we were branded and persecuted, when our names were forgotten and we were seen as less than animals, when our dignity had been stripped away and our most basic human rights ignored... when we were boiled down to a single word: Jew. So yeah, some people take great offence to being called a Jew. "Jewish" however, is not derogatory at all. Just use that instead.