I would start with the following question:
Suppose G-d came to you and revealed Himself without a shadow of a doubt that He was the Creator of everything. He then told you that a certain person had sunk to such an immoral level that their very existence ran contrary to the purpose of the world and that as the Creator of the world (and that person) He was commanding you to kill that person; would you not do it? Would you stand up to the Creator of morality and take the moral high ground?
Now, you may not believe that G-d commanded us to wipe out the seven nations, but that is the narrative that the Torah tells us and the Torah is the single historical source that the Jewish people wiped out the seven nations. Therefore, if you believe the story in its entirety, there is nothing about which you should be ashamed; we were merely advancing the purpose of the word as defined by the Creator of the world. If you don’t believe the story, then of what are you ashamed; nothing happened. If you choose to believe only certain details which seem shameful out of context, then you are clearly looking to find fault and nothing can stop you from doing so.
As far as halachos that differentiate between Jews and non-Jews:
Don’t most people have a different standard for family? We are commanded to treat everyone properly and fairly. Beyond that, we have special privileges for family. A family, as pointed out by someone else, that everyone is free to join. It is not racist to treat your family as special. This is not just a cliche. Look around at Jewish society; we operate as a family. When there is a family celebration, we all rejoice. When there is a tragedy, we all take it personally (events from this past summer can attest to that).
In short- a racist looks down at certain groups. The Jewish people consider one another as family. Big difference.