Why don't you try thinking of 'Jews' as being those who were resident in Judea? That means everybody who lived and paid taxes in the geographic area known as Judea. If you were a devotee of YHWH, and gave credence to the Temple and its priesthood in Jerusalem, then you might be referred to as a 'Hebrew' or an 'Israelite'. But, in Jerusalem, there would have been an admixture of other peoples, both pagan and other Hebraic sectarians, including believers in the likes of the Great Angel, and the Enochians, as well as the neighboring Samaritans. And well all know about the various 'libraries' like those in Qumran, evidencing robust divergent religious traditions. Indeed, only a lifetime earlier, the Parthians had occupied Jerusalem, and lurked just beyond the frontier, so Zoroastrianism would probably have been present, as well. And, of course, after 135 CE, the new temple to Jupiter would rise on Mount Moriah, thanks to the exasperated Latins. What we call Judiasm was not some monolithic belief system....it had a central temple and an active priesthood that was widely resented by much of the local population, as it was a known puppet to the political powers of the day. Most of them would have spoken a Semitic language and acknowledged Semitic customs, even the likes of Herod, who was not a Jew.
What we call 'antisemitism' is a resentment of the teachers of the scriptural interpretations of what became diaspora Judaism and claimed the scriptural underpinnings of the teachings of the Christian sectarians. The 'authorities' of the scriptures denied the Christian interpretation and explicitly excluded Christian teachings as heretical. The antisemitism is reactionary to their exclusion from the congregation.
