What "loses energy" actually means here depends on what kind of redshift you're talking about.
If you're talking about gravitational redshift, because the light is climbing out of the gravity well of a planet or star, there actually is a conserved energy involved--but it's not the one you're thinking of. In this case, there is a time translation symmetry involved (at least if we consider the planet or star to be an isolated system), and the associated conserved energy, from Noether's Theorem, is called "energy at infinity". But, as the name implies, only an observer at rest at infinity will actually measure the light's energy to be that value. An observer at rest at a finite altitude will measure a different value, which decreases with altitude (and approaches the energy at infinity as a limit). So when we say the light "redshifts" in climbing out of the gravity well, what we actually mean is that observers at higher altitudes measure its energy (or frequency) to be lower. In other words, the "energy" that changes with altitude isn't a property of the light alone; it's a property of the interaction of the light with the observer and their measuring device.
If you're talking about cosmological redshifts, due to the expansion of the universe, here there's no time translation symmetry involved and therefore Noether's Theorem doesn't apply and there is indeed no conserved energy at all. But even in this case, the redshift is not a property of the light alone; it's a property of the interaction of the light with a particular reference class of observers (the "comoving" observers who always see the universe as homogeneous and isotropic).
Edit: I just looked into this & there are a few explanations for what is going on. Both general relativity & quantum mechanics are incomplete theories but there are several explanations that account for the seeming losses that seem reasonable to me.
1. Lie groups describe local symmetries. Nothing about the global system
2. From a SR point of view, energy in one reference frame does not have to match energy in another reference frame. Just that in each of those reference frames, the energy is conserved.
3. The conservation/constraint in GR is not energy but the divergence of the stress-energy tensor. The "lost" energy of the photo goes into other elements of the tensor.
4. You can get some global conservations when space time exhibits global symmetries. This doesn't apply to an expanding universe. This does apply to non rotating, non charged black holes. Local symmetries still hold.
The consequence of Noether's theorem is that if a system is time symmetric then energy is conserved. On a global perspective, the universe isn't time symmetric. It has a beginning and an expansion through time. This isn't reversible so energy isn't conserved.
Please explain. Noether's theorem equates global symmetry laws with local conservation laws. The universe does not in fact have global symmetry across time.
You are making the same mistake as OP. Formal models and their associated ontology are not equivalent to reality. If you don't think conservation principles are valid then write a paper & win a prize instead of telling me you know for a fact that there are no global symmetries.
The typical example people use to illustrate that energy isn't conserved is that photons get red-shifted and lose energy in an expanding universe. See this excellent Veritasium video [0].
But there's a much more striking example that highlights just how badly energy conservation can be violated. It's called cosmic inflation. General relativity predicts that if empty space in a 'false vacuum' state will expand exponentially. A false vacuum occurs if empty space has excess energy, which can happen in quantum field theory. But if empty space has excess energy, and more space is being created by expansion, then new energy is being created out of nothing at an exponential rate!
Inflation is currently the best model for what happened before the Big Bang. Space expanded until the false vacuum state decayed, releasing all this free energy to create the big bang.
Alan Guth's book, The Inflationary Universe, is a great book on the topic that is very readable.
One somewhat trivial example is that light loses energy due to redshift since photon energy is proportional to frequency.