Mason is surely correct that ioudaios was a complex term that carried ethnic,
political, cultic, and many other dimensions, even if the jury is still out on the
existence or non-existence of religion in antiquity (see Shaye Cohen, Cynthia
Baker, Seth Schwartz, and Daniel R. Schwartz, who have more nuanced
positions on the matter). But why broaden the referent of Judean from its primary
geographical meaning when there is a perfectly good English word — Jew —
ready to hand? As the Pew Report and many previous surveys and sociological
studies have shown, Jewish identity includes the same elements — including
ethnic, political, cultural, genealogical, and, yes, geographical — that, in
Mason’s view, are conveyed by the Greek terminology. To define Jew solely or
even primarily in religious terms is simply wrong. Further, erasing Jews from
Jewish antiquity, while presumably solving one historical problem, creates
another historical dilemma: how to account for the sudden appearance of Jews
in late antiquity as a fully-formed ethnic and religious group that saw itself —
and was seen by others — as continuous with the ioudaioi of the Greco-Roman
era? Scholars of the Greco-Roman period may not feel called upon to answer
such questions, but the dilemma cannot be ignored.

Adele Reinhartz, ‘The Vanishing Jews of Antiquity’, MRB, 24 June 2014

One thing that has become increasingly clear to me is just how much the socio-religious phenomenon we call ‘Judaism’ was itself a matter of intense debate and negotiation in the first century CE. As Reinhartz goes on to emphasize in her response to Reed, a certain anachronism is perhaps inevitable in historical work, yet I wonder if some approaches don’t risk more distortion than others. In other words, the risks of ‘atomizing’ linguistics, ‘parallelomania’, and anachronistic ‘imposition’ of frameworks are well-known, but I wonder if the shape and scope of certain types of scholarly theses and monographs increases rather than attenuates exposure to these risks.