I do have experience using both C and Rust. Arguably, my C++ is very limited but things like C++ being a relatively large language are well established facts and quite uncontroversial.
It is true that some people resist using anything introduced since they first learned, with a few mired in C. But there is never any need to "agree" on that.
"Bigger binary" is scurrilous propaganda. Compilers nowadays use the same code generator for C and C++: say the same thing, get the same code. Furthermore, optimizers have to guess less at you are trying to do, in C++, so can do a better job. C++ code for the same task is often smaller.
"C programmers often care more about building the best possible software": this is just crude slander.
Finally: "Rust has much better safety guarantees": C++ offers much the same guarantees, where you choose to exercise them.