Natural rights are not moral rights either since they precede and are outside any moral doctrine.
You have a natural right to reject Jesus Christ as your savior. You have no Christian moral right to do so because that is a strictly immoral act. But of course in Muslim morality, you are commanded to reject Christ as God or you are guilty of SHIRK.
Neither government nor religious body nor any individual has the right to infringe on anyone’s natural rights except by permission, that is, your acknowledgement of a moral code.
There is one set of natural rights and it ends at my nose. You may not equate them to any particular moral code.
“Natural rights are not moral rights either since they precede and are outside any moral doctrine.”
No. Natural rights are grounded in the Natural Law - that is the first set of morals.