RTCPeerConnection is an object with certain methods that when called mutate the object (for example, setLocalDescription, addIceCandidate). These methods get called based on received signaling from the other side of a WebRTC connection (like when you receive an offer, or an ice candidate).
Therefore, this object does not seem well-suited for being in a redux store, since the developer doesn't at a first approximation have control over the mutations, and in a redux reducer you can't just create a copy of an RTCPeerConnection as this would eliminate your previous webRTC session.
However, in a WebRTC app that uses React, perhaps different components need access to the RTCPeerConnection object (for instance, maybe it is instantiated on mount of the top level component in the app, but then in some UI component like a modal deep in the tree that accepts a call, you want to call a method on RTCPeerConnection to create an answer to the webRTC offer that was received. Or maybe a deeply nested component needs to initiate a call). Is it the case that the only solution is to pass the object as props down the component tree? Is there no way to use redux with a complex object like this?
UPDATE: considering the answer below about using middleware for handling socket.io, let me reframe my original question: would it make sense, if I have an RTCPeerConnection object as state in a top-level component, to build middleware that that handles dispatch calls that ultimately must receive some way some how a reference to the original RTCPeerConnection to make a method call such as setRemoteDescription?