there's no point at which Jews don't refer to ourselves as a nation/people (עם, אומה), but the Hebrew word for religion (דת) seems to have first appeared in the comparatively later-written Book of Esther, and is a Persian loanword (distantly related to Latin and English "data").
there is, of course, earlier mention of the Jewish people worshipping "other gods" which obviously refers to other religions, but this only goes to show that Jewish peoplehood/nationhood is not dependant upon religion.
or at least that the relationship between the religion and nation is not straightforward
attempts to separate the Jewish nation from the Jewish religion seem to have begun during the transition from feudalism to liberalism. with feudal obligations no longer holding together states, there was a need to get the people to swear allegiance to a "nation" that the state was charged with representing
as such it was said by french revolutionary figures, for example, that there could not be nations within nations...
the suddenly-invented European nation-states felt the need, for whatever reason, to minimize and smooth over the self-identified nations within it, which had been in existence for a very long time
so at the same time, Jews are being asked to assimilate, and often throwing each other under the bus in search of this promise of assimilation
and meanwhile, there are plenty of people who aren't OK with the Jews becoming equals, and want this to end, because they say "this is our country, why should the Jews have a chance at anything? get them out of here and let us have it all"
in parallel, there are places where Jews are doing just fine as a nation within a nation, such as Algeria where they are both Arabs and Jews
and so the French deliberately divide Jews from Arabs, making Jews French citizens and inciting resentment on purpose, to divide the people of their colony
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