It does happen from time to time, I had a customer at work only a few weeks ago with exactly this problem and he was insisting it was a bug in our software and demanding we changed it. He had also posted a similar message to the help forums on the other library. The forum was less polite than I was allowed to be and he got told where to go in very few words, but I was able to persuade him with the question "ok then, what name should we give the function that is guaranteed not to clash with any other software at any time past or future", or something like that.
Actually the problem isn't that difficult to solve, you just have two executables that run in parallel, one linking with one library and one linking with the other, and you define some kind of IPC between the two executables. One can be just a thin wrapper around one of the libraries; you don't necessarily have to split the application down the middle.