Is it ethical to use proprietary (closed-source) software for scientific computation?
I do not think that this is an ethical question in the first place. Reproducibility is not harmed by the requirement that money needs to be spent on buying software or setting up an experiment (or are there open-source particle accelerators?).

While open source solutions are preferable for many reasons, there are clearly cases where using some proprietary software P is appropriate:


When it is known (and has been verified) that P's implementation of method M is correct while the known open-source implementations of M have not (yet) been established as reliable. Conversely, when open-source implementation O is known to give correct results whereas for P this has not been established, then clearly O should be used when there is a choice.
When one can reasonably expect that P is widely available in research institutions (and thus to researchers), like for example certain mathematical / computational packages.
When P allows for a much more (time-/resource-)efficient execution of experiments.
When P is a software package needed anyway to extract / process data from a big-ticket instrument.


Note that I am assuming that P can actually be bought by anyone. If P is not commercially available but rather a closed-source in-house solution then an open-source package is preferable.