Godot blocks any class that inherents the Object class, like RefCounted, from being serialized and sent over as a packet. There is an option in the project settings to allow Objects but this is a security risk to do so as it exposed you to remote code injection.
You can use the custom class still but you will need to sync the individual properties of your input class with the synchronizer by building a replication config programmatically. See here for an example.