The command to hate and wipe out Amalek (including innocent babies) is a troubling one for many modern Jews. You can avoid thinking about the whole thing by arguing that anyway we do not know who is Amalek today, but that doesn’t change the moral dilemma. Rabbi Sacks asks a different question, not about the morality, but about the reason behind the command:
We are commanded not to hate Egypt, but never to forget Amalek. Why the difference? The simplest answer is to recall the rabbis’ statement in The Ethics of the Fathers [5:16]: "If love depends on a specific cause, when the cause ends, so does the love. If love does not depend on a specific cause, then it never ends." The same applies to hate. When hate depends on a specific cause, it ends once the cause disappears. Causeless, baseless hate lasts forever.
That is why are commanded to remember and never forget Amalek, not because the historic people still exists, but because a society of rational actors can sometimes believe that the world is full of rational actors with whom one can negotiate peace. It is not always so.
(Rabbi Sacks: The Face of Evil)
When people hate you for a reason you can address this reason. You can argue, discuss facts, make them understand your point of view, understand theirs, modify circumstances and behaviours, find a compromise, and generally negotiate and come to a solution. In the Torah, these are the Egyptians [maybe not every one of them, but the leaders].
When people just hate you and afterwards come up with reasons for it, there is nothing you can do. If you remove the reason for their hate, they will just find another reason. That is Amalek, they had no dealings with the Israelite and still attacked them. There’s no point in trying to resolve the conflict as there is no reason for it.
The challenge is to see when it’s one or the other and concentrate your energy on those people that have valid reasons for their hate and try to arrive at a common ground.