We use ZeroMQ a bit. It's been pretty much flawless as far as I can see but I get the impression that it's becoming obsolete. Is RabbitMQ a viable replacement?

You should take a look at nng (nanomsg-next-gen) [1], which is a successor to nanomsg, which was a successor to ZeroMQ.

[1]: https://github.com/nanomsg/nng