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We investigate whether the inclusion of baryonic physics influences the formation of thin, coherently rotating planes of satellites such as those seen around the Milky Way and Andromeda. For four Milky Way-mass simulations, each run both as dark matter-only and with baryons included, we are able to identify a planar configuration that significantly maximizes the number of plane satellite members. The maximum plane member satellites are consistently different between the dark matter-only and baryonic versions of the same run due to the fact that satellites are both more likely to be destroyed and to infall later in the baryonic runs. Hence, studying satellite planes in dark matter-only simulations is misleading, because they will be composed of different satellite members than those that would exist if baryons were included. Additionally, the destruction of satellites in the baryonic runs leads to less radially concentrated satellite distributions, a result that is critical to making planes that are statistically significant compared to a random distribution. Since all planes pass through the centre of the galaxy, it is much harder to create a plane of a given height from a random distribution if the satellites have a low radial concentration. We identify Andromeda's low radial satellite concentration as a key reason why the plane in Andromeda is highly significant. Despite this, when corotation is considered, none of the satellite planes identified for the simulated galaxies are as statistically significant as the observed planes around the Milky Way and Andromeda, even in the baryonic runs. [ABSTRACT FROM AUTHOR]