Earlier quoted context omitted.
I agree it shouldn't really matter if there's no C++ features in play, but I suppose third party headers could bite you if they use #ifdef __cplusplus to guard optional C++ extensions on top of their basic C interface. In that case the compiler could be dealing with dramatically more complex code when you build in C++ mode.
Maybe it is similar for the same compiler (but one should check, I suspect C could still be faster), but then there are much more C compilers. For example, TCC is a lot faster than GCC.
1990's compilers were also super fast, they only did optimisation for size, speed, constant propagation, and little else.
Zero code motion, loop unroling, code elision, heap via stack replacement, inlining,...