I can't resist expressing my sympathies that you have to spend time figuring out such a silly requirement...

@paulgarrett The requirement isn't so silly if your paper uses both $\mathsf{\pi}$, the quotient of the circumference of a circle by its diameter, and the $\pi$ groups used to satisfy the conditions for validity of the Buckingham $\pi$ theorem, and you need to be able to tell them apart.

@DanielHatton the purpose of the requirement isn't mentioned in any of the answers. Perhaps you could copy your comment to a new answer.

A pendantic response to a pendantic request would be that you haven't broken any rule since you've not referred to the value 3.14

@DanielHatton I contend that using italic 'pi' and upright 'pi' to mean two different things in the same paper is a far greater sin than using the wrong shape pi for the numerical constant. As for MNRAS, if they want upright pi, then their style file should have redefined \pi to produce the version they want, instead of requiring authors to go in and adjust the markup. The whole point of logical markup is that you're not supposed to have to specify these things in the document source.

@Qsigma If the question had been "why did the editor say this", then my comment might have been convertible into a good answer, but the question was "what does the editor mean", which Massimo Ortolano, nick012000, and Erugg have already answered very well.

@Nobody The rule doesn't originate with MNRAS: as Massimo Ortolano pointed out, it's in the normative sections of an ISO standard (ISO 80000-2). As Erugg mentioned, MNRAS have defined an appropriate macro, \upi (which, in the spirit of it being logical markup not presentational markup, I choose to interpret as an abbreviation of "universal pi", not of "upright pi").

@DanielHatton I was reacting to the claim that upright and italic pi could be used to distinguish between two uses of the symbol pi, which is a terrible idea, no matter who originated it.

@Nobody Yes, ideally one should avoid using both notations in the same document: it should be easy (and is permissible in the ISO standards) just to use some letter(s) other than pi for the Buckingham groups. Nevertheless, using pi for the Buckingham groups is a 104-year-old tradition, and while it continues, using different fonts for the two meanings of pi is less confusing than using the same font for both.

@Nobody Incidentally, what would you do in the harder case where your paper needs to mention both the base of natural logarithms $\mathsf{e}$ and the charge on the positron $e$?

@JBentley Pedantically, a pendantic response/request would be one that is hanging down.

If you resubmit and replace all instances of π with CCCXIV / C, I'll buy you a beer.

@DanielHatton If Euler's number only appeared in expressions like e^{...}, I might let it ride, since the meaning would probably be clear from context, though alternatively one could replace it with exp(...). If having e in mathematical expressions were unavoidable, I'd probably replace the electron charge with q_e or something like that, with a note explaining the reason for the nonstandard notation. I reiterate, it's better to use a nonstandard letter in your notation than to rely on subtle differences (mathcal or blackboard bold excepted, maybe) in typeface to distinguish distinct symbols.

@Nobody Using non-standard symbols just makes it harder reading a paper, and a wise reviewer will tell you to change that symbol (it happened).

@DanielHatton the question is 'What exactly is π in roman?' The answer in part is: "a convention (for choosing fonts or TeX macros) that attempts to distinguish the geometric ratio from the Buckingham groups". I would upvote your answer (I imagine these comments will soon be deleted and your contribution would be lost.)