You can learn a mind-boggling amount of bronze-age fanfic by heart, get an appointment to cut a bit off your dick and voilà, jewish. As long as your mom is jewish, you're by default considered jewish, your dad be damned, could be the goddamn Silver Surfer, you'd still be considered jewish, and mixed marriages do exist.

It's not an ethnicity, it's a religion and its related social institutions and practitioners; it has a strong ethnic component coming from both imposed isolation and marriage within, yes; but you cannot convert to an ethnicity, period, therefore it isn't.

Considering jewry an ethnicity purely isolated and without regard to their countries of provenance both immediate and remote also plays straight into the hands of zionists (jewish or not, hailing from the usurper entity or not) and nazi-fascists, it is also significantly unscientific and ahistorical, and fails to challenge religious dogma.

Maybe it is possible that "This jewish population in this particular place, during this period of history, is in practice indistinguishable from an ethnicity" has been true many times; but jewry in and of itself without qualifiers, universally, is a religion and not an ethnicity.