See, I can't really agree with this, because "evil" is such a broad brush. Imagine a guy who's a member of a powerful aristocracy. This guy has been brought up to believe that it is his right to oppress the underclass. He's aware that they lead horrible lives, and he makes decisions that actively contribute to their suffering. He's knowingly and deliberately profiting from their misery. His peasants sweat and struggle in the fields with barely enough food to get by; his slaves labor in the mines, bringing up gold to enrich his coffers at a terrible cost in lives. He treats them all as disposable and sacrifices them readily to improve his own position.
At the same time, to members of his own elite class, he is the soul of honor, courtesy, and compassion. He is a loyal friend and a stalwart ally. He has a wife and children whom he loves very much and would readily give his life to protect.
I would argue that this is an entirely realistic character and there have been many like him in history. Is he evil? Considering how he treats most of the people around him (the underclass), it's hard to argue otherwise. Yet he is perfectly capable of love and compassion for those he sees as equals.
I would say that no human is fully evil, and very few may be considered to be even fully depraved. And, while I don't doubt the possibility of a character like you describe, I'm not sure I'd go with 'fully realistic' given the dichotomy you portray.
My suspicion is that most priviledged personages who truly were the soul of honor, courtesy, and compassion were at the least troubled by their own relationship to the ones that supported their priviledged existance. If they truly tried to live in an idealized manner toward their peers, they generally probably also tried to hold an idealized relationship with their inferiors. They probably at least tried to act justly, fairly, and properly as they understood the terms of the relation with their slaves. A manorial knight who truly tried to live up to the idealized ethical standard of his day might well profit from the misery of his serfs and think it right for him to do so, but by the same token he couldn't treat them as 'disposable' or cruelly (by the societies standads of cruelty) and also live up to the societies idealized vision of noble behavior. The same would be true of a colonial slave holder. People like Washington who tried to live up to the highest standards of honor as his society understood it, were privately very troubled by the fact that their station was due to the misery of slavery. They certainly wouldn't have treated a slave cruelly as they understood the term, if only for the same reasons that they wouldn't have mistreated a dog or a horse - because they would have considered it to reflect poorly on themselves, to be crass, and to show poor breeding.
On the other hand, if in fact they did treat their inferiors as disposable and cared not a bit for how cruelly they were used, I think you'd typically find that their relationships with their peers were equally calculating and Machivellian. They probably privated mistreated their wives and children as well. They were probably loyal friends and allies only in so far as being a loyal friend and ally advanced their station, and they probably maintained the usual courtesies only in so far as doing so advanced and maintained their station. If they loved their family or anyone else, it was probably only an extension of their own self-love in that the success of their family was in some fashion proof of their own success.
Consider a character like John Rooney in 'Road to Perdition'. All of his apparant noble qualities are exposed as simple self-interest over the course of the narrative. He's not truly loyal to anyone but John Rooney, and will betray just about anyone to protect John Rooney and John Rooney's legacy. He's polite, and loyal, and compassionate only in as much as being percieved to have these characteristics and acting in that manner is good for business.
So I don't deny you the possibility you describe, I'm sure it sometimes happens, but neither do I think such disparate double lives are fully realistic. Cruelty and callousness tends to have a coarsening effect, and conversely compassion not born of simple self-interest towards anyone tends to make it harder to be cruel to anyone.
Which brings us back to the beginning. No human is fully evil. Even the worst of us don't usually desire evil ends, but rather desire good things and try to accomplish them with evil. It's difficult for us to imagine someone desiring evil, suffering, and destruction as an end unto itself.