I'll stick my neck out and say that every technical position requires a sound understanding of bitwise operations.
And I have an anecdote that indirectly addresses the topic.
January 2007 I was in Cochin, India, recruiting for permanent development staff. Since I wasn't involved in the preliminary screening of candidates I had no idea what standard to expect so I had prepared a range of questions and topics ranging from simple understanding of binary and hexidecimal through to architecture, design, and project management.
When I discussed my approach with the Indian HR guy I was (gently) chided for pitching too low. He made it clear that my questions about hex would possibly be construed as an insult to the candidates experience or education.
But my experience of interviewing hundreds of candidates in the UK had fixed in me a conviction that it wasn't possible to pitch too low. My opinion was and still is that if it becomes obvious a candidate is well qualified then it's simple and easy to adjust the level of discussion. I've never had anyone express feelings of being insulted, on the contrary I think a well qualified candidate might feel relieved at a flying start to the interview. It also helps to break the ice and build a rapport needed for a meaningful interview. On the other hand, unqualified candidates usually fall at these lower hurdles.
But not wanting to completely ignore local advice I cautiously decided to include my basic interview topics, and was quite prepared to abandon them if they didn't work.
As the interviews progressed I was glad that I started at that level. It didn't offend anyone, and unsuitable candidates were easily identified.
This is not to say that I expect candidates to deal with bit-twiddling day to day, but whatever the language a sound understanding of the fundamentals of programming is essential. Even developers at the higher levels of abstraction are exposed to hex on a regular basis (RGB values, for example). Parroting stuff you find on the net will only help to the extent that things work perfectly first time.
But for developers starting out in the past five years I believe it's all too easy to gloss over the fundamentals, cosseted by well intentioned IDEs and the meme of "codeless" programming. The Visual Studio installation spash screens boast about developing without writing code. Indeed, does Visual Studio rot the mind?