The weird part is precisely this: "you can get back to a state where you can no longer tell what the outcome of the 'measurement' was." In other words, at lunchtime you believed that a horizontally polarised photon hit your nose at 10am in morning, and you were right. Now it's dinner time, you don't believe that, and you would be wrong if you did. If the Everett interpretation doesn't pose a massive challenge to your ideas about reality and human identity, you haven't understood it. There are physics professors who picture photons choosing which way to go at a beam splitter, then transmitting the news backwards in time, because that seems more plausible to them.
Of course, interpretations are not science. Everyone agrees how an experiment would go: any attempt to reverse the interaction of the photon with your nose and brain would fail, because thermodynamics. From a purely scientific viewpoint, it simply doesn't matter how many other yous are superposed in parallel universes, because their existence or lack of it has no consequences that (any of?) you can observe. But scientists are as fascinated by this as everyone else is.