There is an interesting history behind this. When Christian missionaries first arrived in India to spread their religion (in the late 1700s/1800s) they were initially unable to make much progress, but then found success among lower caste Indians by promising them a life of equality. So the vast majority of Christian converts in India are from these castes.
Mangalorean Catholics for instance are mostly Saraswat Brahmins who converted around 1700s https://en.wikipedia.org/wiki/Mangalorean_Catholics
It's also a question that's very easy to ask in good faith while making small talk, which makes it noticeably dangerous.
I am in tech management (also a recovering attorney) who routinely conducts interviews, and it is perfectly acceptable to ask where someone is from in a professional setting.
The unacceptable part, as OP at least hints at, is using the response as a proxy for some other verboten criteria or perhaps to kickoff an overly intrusive line of questioning.
These behaviors are odious on their own and why HR should be explicit in training against antipatterns, not spreading meaningless FUD which miss the point and permit bad habits to foster elsewhere.
It’s really inane that modern software recruiting claims to focus on getting a proper picture of the whole candidate , yet untrained interviewers counterfeit the whole endeavor thinking they’re politically correct because they’re afraid to ask anything but the same broken whiteboard questions.
Whenever I mention to a team member that I was interviewing somebody for a position on our team, they always ask: "are they in India?" I had never really wondered why before.
That is not always correct (but is true in most cases). There are caste-neutral names in India - especially Tamil Nadu. But that itself is a hint about the person's caste, since it is adopted mostly by people of the unprivileged caste.
> Is this something that comes up in conversation among Indians?
It starts casually with "where are you from?" and the questions get more invasive.
> Do names tend to correlate to you caste?
In India, yes it does family name is derived from caste. I had some friends adopt English names to get from under their caste names. So quite a few Johnsons, Smiths, Matthews, Pauls out there.