What do you mean by "production ready" here exactly? In a web browser context, the JS engine is expected to have a high performance optimising JIT compiler. Do the existing Rust JS engines have that?
I honestly don't know, but they do say "production ready" on their marketing pages, so...
For an example of what I mean, see JetCrab: https://jetcrab.com
There's something to be said for the security benefits of not having a JIT though. Especially if you've used Rust for the engine you should have pretty solid security.