Is not the law, it can be changed by executive fiat. That is by observing the proper procedure, publishing the proposed change or new regulation, and then taking public input (which can be ignored). Then after the proper amount of time, it's the new regulation.
Their right to vote and all other rights are lost and only remain by the grace of the legislature.
Including presumably their right to speak in public, their right to publish what they wish, and their right to exercise their religion?
Yeah, it is.
"it can be changed by executive fiat."
No. You ignored what I said about it above. The definition in 27CFR411 is based on the way medical opinions and those adjudications and commitments work in the US, not how the bureaucrats think it ought to be.
"Including presumably their right to speak in public, their right to publish what they wish, and their right to exercise their religion?"
That's correct. Note that in many states a felon can not profit from their crime by writing and speaking about it. The courts and legislatures have otherwise found that restricting their speech has no justification, or significant effect. Note that punishment is not a justification here. The idea is that a felon has proved some propensity for criminal behavior and an unwillingless to control it. With regard to religion, the courts have held that one's religion should not be largely stripped away, even in prison.
IOWs shooting off one's mouth has no real physical consequences with regard to health, safety, ect... Shooting off a gun does.