I think the language we'd use around person C depends on the context. "Gay" and "black" are fine to say at a bar but weird in a more formal setting like a courtroom or company-wide presentation. There's a ton of other language like this, nobody is upset that they can't tell fart jokes in a courtroom.
If person A describes person B as homosexual" or "African American" instead of "gay" or "black" instead of in order to not offend person C who is straight and white is that an example of being polite or political correctness?
I would say the latter.