I think the minimum amount of understanding needed to grasp MWI is understanding the double slit experiment. The interference pattern is real, thus the waves are real, but we only experience one measurable outcome where a photon lands in a specific location. The probabilistic part is not which outcome happens but which outcome your reality follows.
My point is that analogy is influenced by fiction. It is too easy to attach concepts from fiction to the double slit experiment. Saying things like "which outcome your reality follows" are humane experiences overlapped on to the experiment, not something that arises from the experiment itself. Nor something that arises from the math.
I will humbly disagree. I don't think fiction plays into it much, more the other way around. I think the 'multiple universes' ideas in fiction are likely to have been inspired by those experimental results. Just knowing how the double slit experiment works made me consider that every wavefunction might result in an infinite number of outcomes that never interact again, despite always having a dim view of fiction with parallel worlds. The fictional multiverses still aren't plausible, since usually there is some interaction between the different worlds, and they don't well represent the continuous nature of things, but it seems a little less dumb conceptually having learned about that experiment, quantum erasure, etc.