The Torah forbids racism.
Rav Yaakov Kamenetzky in his book on Chumash - Emes L'Yaakov (Parshas Noach 9:25) states emphatically that the Torah is not racist. Basing himself off the Gemara in Sanhedrin (37a) which states:
לפיכך נברא אדם יחידי ללמדך ... מפני שלום הבריות שלא יאמר אדם לחבירו
אבא גדול מאביך
Thus, Man was created alone initially in order to teach respect for
humanity, for man cannot say "my father is greater than your father"
The Torah does not accept the belief that one race is greater due to their lineage and DNA is more superior to another group. However, the Torah does recognize the differences between races, in that those differences have been encouraged and cultivated throughout the generations to the extent that those traits are programmed into the makeup of the person. The Torah differentiates groups based on the character and morals of the people, and that if those traits are negative, then the people are to be viewe negativly. However, these attributes are not "inherent" in the person, and through character development ie. working on oneself to be more G-dly and holy, the person can break out from the bad traits they were raised.
That is not called racism, because race in the eyes of G-d and His Torah is inconsequential, we don't hate them because of their lineage or make-up, rather it is the innate traits and mores of that particular group. We Jews believe that one can rise above their externally influenced traits. Whether through the acceptance of the Sheva Mitzvos Bnei Noach - The Seven Noahide Laws, or through full-fledged conversion to Judaism. The Torah believes in problems with certain cultures, which cause problems for people raised in those cultures, but have nothing to do with racial heredity.
Rav Yaakov makes it very clear in his piece:
ודאי זה אין משום שדת ישראל גזענית היא חס ושלום, אלא שאנו אומרים
שמכיון שאנו ירשנו מדות מהוגנות וישרות מאבירי דעה כאלו כמו אברהם ויצחק
ויעקב...ממילא אנו בני מעלה יותר משאר העמים, כי הרי אנו שיפרנו את
עצמינו במדות טובות ובהתקרבות להשי"ת
Rav Moshe Feinstein also echoed such a sentiment regarding the Falasha tribe who claimed Jewish lineage:
As you mentioned, they should not be brought to the Land of Israel*
unless they have underdone a conversion**, in order to not increase
the concern for assimilation [i.e., intermarriage with Jews who do not
have a doubt regarding their Jewish status and also a weakening of the
faith of Ethiopian Jews themselves]. But if they have legally
converted, and as I have heard they are doing, we shall consider them
like all Jews, and one must assist them and support them for all needs
of livelihood, both physically and spiritually. And I suffered great
anguish because I have heard there are those in Israel who are not
drawing them close in spiritual matters and are causing, G-d forbid,
that they might be lost from Judaism. And it seems to me these people
are behaving so only because the color of the Falashas' skin is black.
It is obvious that one must draw them close, not only because they are
no worse than the rest of the Jews – and because there is no
distinction in practical application of the law because they are black
– but also because one can say perhaps they are gerim [converts], and
are therefore included in the mitzva "and you shall love the convert."
Possibly clearer version here