Out of universe: Read the Nemesis the Warlock series by 2000AD. It's a comic strip about a psyker alien (Nemesis) on the world of Termight (MIGHTy TERra) being hunted by a xenophobic Grand Inquisitor and his army of Terminators. You'll also see, among other things, that the upright arrow used as the symbol for Marine tactical squads was lifted from the stylized graffiti image of a nuclear blast that appears throughout this strip.
The xenophobia of the Imperium is really just an element of grimdark humor 'borrowed' from Nemesis, much like how Horus is modeled on the Traitor General from Rogue Trooper, and the worship of Chaos was inspired by the Khaos religion of the ABC Warriors (all of these being 2000AD books). In other words, it's an existing trope taken to darkly comic extremes in 40k.
In universe: remember that besides the playable aliens of 40k, there's tons more, including psychic mind-slavers and entire death-worlds filled with various alien species of varying levels of intelligence and sentience. Beyond memories of alien slavers and slaughterers, you're also dealing with aliens still blocking access to habitable planets, or effectively making potentially habitable planets into death-worlds or otherwise extremely inhospitable worlds, all of which undermine the Manifest Destiny of the Imperium's desire to control the galaxy.
Also remember: an alien species (the Eldar) gave birth to Slaanesh and essentially were ground zero for a massive warp blast that obliterated multiple entire sectors of real space. The lore tends to focus on all the dead Eldar that were created, but it's likely that there were remnant human colonies caught up in what's now the Eye of Terror. So much like how human psykers cannot be allowed to exist uncontrolled because a single one could endanger an entire world, so too can psychic aliens could cause the destruction of an entire system or sector if they were allowed to live alongside (close or remotely) Imperial systems or in the same sectors/regions.
Finally remember: the Emperor has seen how easily humans are to divide amongst themselves. Xenos hatred is, at least short term, an effective means of unifying and directing the human need to judge and hate outward towards a non-Imperial target whether than risking them turning it on each other, especially when it's already easy (and happening) for divisions between Terra and non-Terrans as worlds are brought into compliance (let alone the divisions within the Legions between Terran and non-Terran recruits).
Post-finally remember (lol, sorry): alien tech already complicates the barely-understood human tech that the Imperium is recovering during the Great Crusade, whether in side by side comparison or when it gets blended into it. It's - especially to the Mechanicum - often proof that aliens are equally or sometimes more competent than the Imperium is, especially when the aliens know how their energy/plasma/gravity/time-warp tech works and the Imperium is struggling to reverse-engineer standardized blueprints to tractor-tanks and weaponized chainsaws. While the Emperor of course directed a lot of the anti-xeno agenda, he wouldn't have been alone - the Priests of Mars (as well as some of the liberated worlds) would have had their own reasons to hate the alien as well.