historical-changetoponyms
Reading contemporary histories of the First World War, I noticed that at the start the nation in the Balkans is referred to as Servia, but in numbers published after the back half of 1916, it has turned into Serbia.
Is there any particular reason for this?
Consulting Google NGrams gives:-
which seems to correspond to my observation.
Edit Replaced Google NGram with version using capitalised names, as suggested by Steven Littman; the result makes rather more sense.
Always taking a bit of a chance using the Internet to answer an Internet question, but Daily Writing Tips says that not only are while and whilst interchangeable, but that in fact while is the original version. The very authoritative Michael Quinion backs this up on World Wide Words (and that is a site well worth visiting for anyone interested in the English language).
So I think your question proceeds from a false premise: they haven't come to be used to mean the same thing, they do mean the same thing, and there is nothing wrong with using while in all cases. (And to answer the question that wasn't asked, since it is shorter than whilst and clearly understood by US as well as British English-speakers, I'd say stick with while every time.)
Here is a comparative graph from Google Books ngram utility:
Whether this graph confirms your hypothesis regarding the rise of political correctness (per your tag) depends of course on what that hypothesis is, but also and perhaps more interestingly on what your definition of political correctness is.
Best Answer
From a not credible source:
and from another similar source :
and finally a credible one could be find at http://paperspast.natlib.govt.nz/cgi-bin/paperspast?a=d&d=NOT19150305.2.51