This is completely misguided. People who call themselves C/C++ Programmers are basically developers who are proficient in Systems Programming and not necessarily C or C++. It just happens to be that C and C++ were the only primetime options until the likes of Go and Rust entered the scene.

Also if you know C++ to a decent enough extent, you are going to have a certain level of command over C too. And there is no reason why calling yourself a C/C++ Programmer should undermine your proficiency in either of those languages.

Broad generalizations are generally bad.