Honor your father and your mother.
כבד את-אביך ואת-אמך
Shemot 20:12, Aseret HaDibrot
This commandment is not unique to Jewish or Judaic-based traditions. Confucianism, Native American spirituality, shamanism and even various forms of paganism each teach its practitioners to "honor the ancestors".
There are no "purebred" human beings. There is no such thing as a "pure" Jewish or Celtic or American identity or tradition. All of us have forebears of non-Jewish or non-Celtic or non-American heritage. To honor one's parents, to honor one's ancestors, is to honor them all.
Honoring one's ancestors is not a sentimental exercise with the aim to induce feelings of being special or superior. It isn't to praise one's ethnicity or one particular "type" of human being. What is it then?
It means coming face to face with who you are and where you came from. More importantly, it means to work to heal the wounds caused by those who came before us. It means to work to resolve the pain introduced into the world by those in our family trees whose behavior or values we may not embrace, whether they be Nazi sympathizers, Jewish capos or exterminators of pagan cultures. No people, I repeat, no people, is without a dark history that needs correction.
Honoring the ancestors is to work to make those corrections. This is why "honoring one's parents" is the hardest mitzvah to do.