I think (but could be wrong) that error will always be in the startup log of Rust. I've just tested by installing another Rust Server Docker and I was able to connect to RCON (and it also displayed that error during the startup log). So I suspect something else is going on here, potentially to do with network/routing.
Naturally I haven't changed my port forwards or anything when testing - so there must be something in your Docker that I need to tweak.
Could it be that the network type is BRIDGE whereas the other docker is in HOST?