Dark matter affects some galaxies, but the rotation of others is completely explained by the observable matter. Why would one galaxy be influenced by its many worlds twins, but not another?

Sci-fi plot concept answer: because one galaxy is populated by sentient life, and the other isn’t.

Quarantine by Greg Egan explores this concept (the many-worlds theory, without the dark matter).

Well because that galaxy in that position might be a low probability event - not many universes have that galaxy at that position. So therefore that galaxy appears to have less dark matter.

The Milky Way and other similar galaxies look like spiral drawn in a thick 2D disk.

The dark matter halo looks like an invisible 3D ball around the thick 2D disk.

Something like https://www.google.com/search?q=dark+matter+halo&tbm=isch

I thought that the main mechanism that produces the 2D disk of matter in galaxies was gravity, and that dark matter is equally affected by gravity as normal matter? What is the prevailing theory as to why dark matter accretion around galaxies is different from normal matter?

(edit: to answer my own question, the rabbit hole starts here: https://physics.stackexchange.com/questions/485214/ -- basically, accretion happens because light matter can radiate and shed its (kinetic) energy that way. Dark matter does not radiate so it remains in a higher-energy state)