The Empire did practice racial segregation in some places, as well as slavery, and the pro-human anti-alien policies were used to drum up popularity in the wealthy core worlds which are mostly human.
Coruscant had segregation, aliens were not usually permitted into the upper areas of the city-planet. Part of Leia's backstory involves her intervening with an incident of police brutality on a wealthy alien (I think a Quarren, but I might be misremembering) trying to go to the upper levels of Coruscant. Many alien races were enslaved in large quantities by the empire, while humans were usually only enslaved if they came from the empire's outskirts or were criminals.
The seeds for this were set in the Clone Wars, much of the leadership of the CIS were aliens. The Trade Federation, the Techno-Union, the Geonosians, so on and so forth, were all alien dominated groups or governments*. This made it easy to drum up anti-alien bigotry at the same time as anti-droid bigotry, both of which served Palpatine's purposes of consolidating power into the wealthy human dominated core worlds.
Many races that were pro-jedi and anti-Palpatine found themselves discredited, politically marginalised and oppressed. The Wookies are a prime example, with the empire enslaving them en masse and promoting a stereotype of them as brutish primitives.
Palpatine himself probably wasn't speciest, he had friends and advisors who were aliens, but he used speciesm as a tool to help shape the narrative of the empire and cement his position.
*There were human dominated planets in the CIS, but they, along with most of the CIS's actual planetary governments were kept in the dark and sidelined by the Confederate war council which was almost entirely aliens lead by Dooku.