Is energy always conserved?

This is confusing. You said that Emmy proved that symmetry in physical laws give rise to conservation laws (which is correct). Then you said that Einstein's theory of general relativity showed that spacetime can change, but next comes the absolute leap in logic. You say that because spacetime is changing, then the laws of physics can change too. Why? I see no connection between the two. It is perfectly compatible to say that spacetime changes but the laws of physics remain constant across space and time. It seems even more odd to use Einstein here given that the principle of relativity is THE fundmental postulate from which we can build up everything in his theory, and that principle says that the laws of physics are the same across all reference frames (i.e. no matter where or when you are). What's happening!?!