"In Rust We Trust" is an affectionate phrase that glorifies old (or rusty) things.
Below is the description of a business called "In Rust We Trust" which pretty much explains what the phrase means:
We LOVE different, crazy funky, rusty, dirty used and abused items! We love that you can create so much with so little! We love scourying the internet to find the latest and greatest ideas on refinishing, distressing and finding new life in old items!
The phrase, which is a rip off of the hugely popular "In God We Trust" motto, is frequently used by individuals who love transforming old/vintage and rusty objects into art, making them new again.
Bringing back old rusted pieces to life again is somewhat like uncovering its history - who used them, what were they used for and what did they look like when they were new.
Of interest, checkout 22 Companies With Really Catchy Slogans & Brand Taglines from Hubspot.com.