Engineering is all about trade offs. Saying everything should be re-written in Rust is bad engineering. There are valid reasons to keep writing C code. Your project may have one of those. It always depends.
That said, for new projects today, in general, I'd prefer to see them started with Rust than started with C, if all else is equal. It always depends.
Possibly the largest and most well-known C++ project being re-written in Rust is Firefox. Its next release in a few weeks, 57, contains a host of improvements, but one of the ones I'm most excited about is Stylo. It's Servo's CSS handling, but in Firefox. This means that hundreds of millions of people will be using code written in Rust, and I find it thrilling.