Speaking out-of-universe, whenever you want to create a side that needs to be seen immediately and forcefully as the enemy, the classic model is the Nazis. Nazis are very easy for audiences to hate, and so anything that evokes that imagery is common fodder for large organized enemy factions. Racism was one of the Nazis' hallmarks, and therefore, whether implied or explicit, it is generally found in most sci-fi and fantasy concerning people you are supposed to hate.
Additionally, the original movie had a limited budget, and all three movies were originally produced before the digital effects revolution. Also, Lucas was specifically trying to avoid the Roddenberry universe, where every week you saw a new race that was basically human with certain tweaks. So, prosthetic makeup was rarely used; I can think of only two significant characters in the original movie that used it, the guy who gets in Luke's face at the bar and Chewie. Pretty much every other character in the original trilogy is a puppet, a guy in a rubber mask, fur coat or tin can, or human. Only the last category had the ability to really act on-set, with facial expressions and sustained speech, so most of the characters in the original trilogy, even on the rebel side, are human(oid). The exceptions are notable; Yoda (puppet), Jabba (puppet with human inside), Ackbar (animatronic mask), Bib Fortuna (Jabba's majordomo, human with prosthetics), and yes they are all non-Empire, but when you really think of it, even the rebels are disproportionately human. It wasn't until the Special Editions, and then Episodes 1-3, that you started seeing CG and highly altered-humanoid character races begin to appear with significant screen time (Jar-Jar, the CG Yoda and droids, the Trade Federation, fantastical animals, etc etc).
In-universe, the near-human exclusivity would probably have stemmed from the fact that Palpatine would have chosen people he trusted (or at least could manipulate) as his high command, who would have chosen their cronies from their personal circles, and so on. From a psychology standpoint those people would have been picked because they were "similar to me" from the perspective of those doing the choosing. In addition, as the Empire tightened its grip, those closest to the Empire's base of power in Coruscant (and thus likely colonized by similar-looking races) would have been more likely to align with the Empire, while those lying further out in the galaxy would have been more likely to break away (even the Old Republic didn't control the entire known galaxy; Tattoine was effectively independent).