Asking about the background of the interviewer is somewhat of a taboo question [1]. However, knowing the background (educational institution, degree) of the people in the company can help the candidate assess the right fit. Is there a diplomatic, indirect way to do that?
I can't see how you could possibly ask that diplomatically ("So tell me... what kind of people work here?"), nor why on earth you'd need to do: poking around the profiles of the company's employees on LinkedIn for a few minutes should tell you all you need to know.
That said, I agree with Joe's comment: I don't really see what useful information you would get from seeing if a company's hires have PhDs from Harvard or whether they're self-taught, most successful companies that are large enough will have both. And if this was a blocker for the company thinking of hiring you, you wouldn't even get as far as the interview.
Not a great question to directly, but that information is easily available through Google, LinkedIn, company website, glassdoor, etc. This should be part of your homework BEFORE you show up for an interview.
If for some reason you can't get what you need through online channels there are a bunch of non-direct questions that can help flushing this out: "How does working here compare to other places you have worked before?". "What's important in a candidates personality and/or background to be successful here??
