What you seem to want is a species whose culture is devoid of prejudice, but your proposed solution of removing all differences is impractical. If every member of the species is indistinguishable, then that would imply they have little to no genetic diversity and this is undesirable if the species is to survive for a long period of time. Furthermore, prejudice may be based on socioeconomic factors and differences of opinion. Addressing this would require removing individuality, which isn't impossible but means their psychology would be fundamentally alien to our own. I propose a few alternative solutions.
The species as a whole lacks any kind of individuality: they all think and act as one. Since they cannot have differences of opinion, prejudice is impossible (anymore than our brains may be prejudiced against our limbs and internal organs).
An explanation for this that most readily comes to mind is that the species is eusocial, like some kinds of insects. The species is divided into castes that perform different but equally vital roles, such as labor, combat, reproduction and complex thought.
An example of this are the various "bug" civilizations in science fiction, such as Pseudo-arachnids in Starship Troopers, Formics in Ender's Game, and Tyranids in Warhammer 40,000.
The species communicates by exchanging thoughts, feelings and memories directly rather than through imperfect intermediaries like writing and speech. This overcomes one of the vital enablers of prejudice: lack of empathy. Since this method of communication is so efficient, compromise is much easier to achieve and prejudice has difficulty taking hold. Any prejudices that survive will probably be held by the entire species and then only because they all agreed it is necessary.
Depending of the degree of exchange they might not develop individuality or consciousness in the way humans understand it. At the extreme end they might consider their physical bodies expendable so long as most of their knowledge and memories are preserved elsewhere.
An example of such a species would be the "Super Happy People" in the web novella Three Worlds Collide.
Eugenics and brainwashing
This is probably the exact thing you didn't want, but one possibility is that the species practices an extreme form of eugenics. Long ago most differences in appearance and opinion were wiped out (perhaps by natural disaster, perhaps by war), then the survivors used genetic engineering and brainwashing to create a truly homogeneous society.
An example of such a society would be the Fords in Brave New World, the Borg in Star Trek, and the cenobites in Hellraiser.