babel-register can be used in production and I also did that at a company I worked for, but I wouldn't recommend to do it if it can be avoided.

What we mean by not production ready are more the technical limitations that babel-register has and that cannot be avoided which is why we do not recommend to use it for critical infrastructure.

James is correct that babel-register is build to transpile the code at runtime and in order to do that it needs to load babel, needs to load the sourcemap mapping module and also needs to keep the transpiled modules in the cache. This makes your NodeJS script have a longer startup time, and also consume more memory. Especially if you have a lot of files that babel-register needs to transpile this can lead to massive increase in runtime and memory.

An alternative recommended way is to use babel-cli and compile all the files for NodeJS during your build process or deployment beforehand and then use these files to run you NodeJS application. This way you don't need to load babel during runtime or hold anything in cache and you get the full performance that NodeJS can offer.