At the beginning of quantum computation, David Deutsch made a strong claim that the Many Worlds interpretation of quantum theory was at the foundation of his ability to do what he did. There was a lot of interest in his claim, and Many Worlds had something of a resurgence at the time. Amongst other strong claims, I'm particularly aware that Chris Fuchs has pressed a Bayesian perspective that is rather different from the Many Worlds interpretation.
My perception, however, is that quantum computation/information/communication is now much less in thrall to any particular interpretation, unless we say there is such a thing as the minimalist interpretation. It seems that most quantum computation work is reported in journals in as close to the unadorned Fock space formalism of quantum optics as possible, often cut down to a small, finite number of harmonic oscillators, in one of the many formalisms and ansätze of statistical or condensed matter Physics, or, of course, the discussion revolves around qubits. Nonetheless, quantum information is not called quantum particle information —it's not part of particle physics— and the Bell and other inequalities that form the basis of the general rejection of classical particle physics are central instead of being as peripheral as they often seem in particle physics, so it seems, to me, that there is at least something of a change of perception, of zeitgeist, if you will.
Quantum computation for a long time was a subject of keen interest in the academic quantum foundations conferences that I went to back in the day.
Is that interest still there? As Peter Shor points out in a comment, this interest is still there, but Is any of that interest felt in the wider Physics community that has relatively little practical interest in quantum foundations? [Peter Shor Answered that too —in a way that agrees with my prejudices, so it must be right— while I was writing the EDIT below, which tries to address one way in which I think the zeitgeist is being affected.]
EDIT: I suppose a significant number of Physicists will occasionally read PRL articles on quantum information that are highlighted by the editors, and it would be hard to avoid all Scientific American, New Scientist, and Nature articles on the subject. Someone considering grant sources would presumably at least briefly consider whether their work could be applied to QI (I'm bored already with the comp../inf../comm..) and occasionally talk to the QI group at their Institution (almost everybody has one of those by now, right?). Insofar as they do, then it seems inevitable that some QI viewpoints must be increasingly out there. Bell's theorem is surely more a topic of informed discussion than it was 20 years ago. To make the question more specific, and to include my bias in a more explicitly leading way, Do people agree with the implication of my second paragraph that “particles” are less in the air than they were in the heyday of Particle Physics? [If you not unreasonably think that's too specific, feel free to Answer the original and more general Question of the title. The more specific Question still admits at least evidence of the sort given by Peter Shor, and shouldn't be thought of or addressed as only a Yes/No question.]
Hat Tip to Roy Simpson for this Question (his is the credit, mine is the blame).