The assertion that Halacha b'yadu'a Esav soneh l'Yaakov is related to general Antisemitism, has no source in Chazal. As Rashi brings it down in Chumash (Bereishis 33:4), it is strictly a statement concerning the relationship between the two brothers. There is no basis for its extrapolation to broader groups of people. From my perspective, bandying the statement around obfuscates rather than clarifies, as it makes Antisemitism some intrinsic emotion innate to non-Jews. Were that indeed the case, it would seem unjust to punish those who are predisposed to it. It is also not appropriate to link this Chazal to the profound derashah (Shabbos 89a) concerning the sinah that came down at Sinai. The Likkutei Torah (R' Schneur Zalman of Liadi) explains that this derashah refers to the hatred that the Jews received at Sinai - towards the vile traits of pagan nations (see Rashi ad loc., who also seems to have understood the Gemara in that vein).
Moreover, it seems very difficult to reconcile this notion of pre-programmed detestation of Jews with our mission of Ohr la'Goyim:
...ועיקר סיבה זו שיהא רוב חיותנו בגלות, דהקב"ה גילה לאברהם אשר נוצרו בניו להיות לאור גויים, וזה אי אפשר רק כשהם מפוזרים בגלות
|הנצי"ב, העמק דבר לבראשית מז כח|