Perhaps you think that MW says that, at each "branching", a distinct universe, made out of distinct material stuff, is created out of nothing. That would be a violation of conservation, but that's not what MW says.

That is what the Wikipedia entry on many-worlds describes it as saying, as I read it.

It further says:

Common objections and misconceptions:

• Conservation of energy is grossly violated if at every instant near-infinite amounts of new matter are generated to create the new universes.

MWI response: Conservation of energy is not violated since the energy of each branch has to be weighted by its probability, according to the standard formula for the conservation of energy in quantum theory. This results in the total energy of the multiverse being conserved.

Please remember, my larger point is not to argue for or against many worlds. My subsidiary point is that many worlds is considered an acceptable view to hold, and therefore not considered dualism; even though it appears - to most people, even if not to MW experts - to fail the only sensible test I was able to come up with to distinguish good dualism from bad dualism.

• It does not matter whether experts currently agree that MWI actually does or does not violate the conservation of energy or not. It only matters that many people who would say, if asked, that MW violates conservation of energy, would nonetheless not call it dualism.
• My conclusion was not that many worlds is wrong; my conclusion was that the concept of "dualism" is bankrupt.

More generally, not to Tyrrell specifically, but to the multitudes aggressively down-voting this post: Relax! I didn't say anything bad about EY! Just follow the chain of reasoning, people; stop hyperfocusing on phrases that upset you, and getting upset because something you like was used in the same context as something you don't like.