They're not all aligned on the same plane, they're somewhat aligned along the matter filaments and sheets (including the suspected dark matter) that make up the large scale structure of the universe.
"Galaxies are not distributed randomly in the cosmic web but are instead arranged in filaments and sheets surrounding cosmic voids.
[...snip...]
We found evidence that the spin axes of bright spiral galaxies have a weak tendency to be aligned parallel to filaments. For elliptical/S0 galaxies, we have a statistically significant result that their spin axes are aligned preferentially perpendicular to the host filaments;..."
"Galaxy shapes are not randomly oriented, rather they are statistically aligned in a way that can depend on formation environment, history and galaxy type."
"Galaxies are not distributed randomly in the cosmic web but are instead arranged in filaments and sheets surrounding cosmic voids. [...snip...] We found evidence that the spin axes of bright spiral galaxies have a weak tendency to be aligned parallel to filaments. For elliptical/S0 galaxies, we have a statistically significant result that their spin axes are aligned preferentially perpendicular to the host filaments;..."
https://arxiv.org/pdf/1207.0068.pdf
"Galaxy shapes are not randomly oriented, rather they are statistically aligned in a way that can depend on formation environment, history and galaxy type."
https://arxiv.org/pdf/1504.05465.pdf
https://ned.ipac.caltech.edu/level5/March15/Joachimi/Joachim...