The basic census information is Crown Copyright. The fact that FindMyPast have made digital copies of the pages is a separate issue. It is questionable whether these images attract a separate copyright since they were made by an entirely mechanical process (there are videos showing how this was done on Youtube), and therefore there is insufficient human creativity involved to bring about a new copyright in the images. The reason this is debatable is that FindMyPast would no doubt argue that the human element comes from the preparatory steps of preparing the pages (conservation etc) and the transcription afterwards. However neither of these activities actually impact on the making of the digital images, and thus according to guidance issued by the Government's Intellectual Property Office, the images are unlikely to attract copyright ( see the fifth paragraph of this
guidance notice). The fact that FindMyPast (or BrightSolid) claim copyright doesn't make any difference as it's not illegal to claim it even when it doesn't actually exist. A court would have to decide the issue.
The transcriptions themselves are probably subject to copyright since the individuals doing the work have to use skill and experience to decide what the handwriting says, and this is evidence of their creative decisions. This similar to the work of a translator who most definitely is entitled to copyright in their work.
Because of the overall uncertainty, the rules that RootsChat have adopted rightly err on the side of caution.