Well, it certainly isn’t racially derogatory, so it couldn’t possibly be anti-Semitic per se.
(People often say anti-Semitic when they really mean anti-Jewish, but that’s largely because Hitler insisted on the two concepts thanks to his reading of evolutionary theory.)
Is it anti-Jewish? No, the whole thrust of the Epistle to the Hebrews is to explain how Christ fulfills the promises of Judaism in ways more superior than Moses, angels, Jewish priests, or even Melchizedek. (All of whom were highly promoted by the Jewish philosopher Philo, who lived and wrote at the time of Christ’s ministry. The author’s topical scope is an indication he is writing to a group of Christians who were once Philonic Jews, and/or in strong contact with Philonic Jews, and/or that the author himself was once a Philonic Jew. I tend to agree with Ronald Nash that this points toward the author being Apollos, but that’s kind of speculative.)
Naturally, insofar as a Jew is anti-Christian then any text promoting Jesus as the Christ will be anti-Jewish by comparison, but only in that limited regard. But that isn’t anti-Semitism.
Anyway, the author’s argument is not that the Levitical priesthood is worth nothing, but that the priesthood of Melchizedek is inherently superior somehow (in a way fulfilled by Christ) by the testimony of the actions of the First Official Jew himself, Abraham, who gave a tithe to Mel. Thus Levi and his descendants, regarded by the author as present in Abraham’s loins (an ancient biological concept, which also helps explain how to understand statements that all have sinned in Adam), acknowledge the religious superiority of the Melchizedekian priesthood.
(I’m actually a little surprised that the Hebraist doesn’t spend more time focusing on the fact that Mel offers a sacrifice consisting of only bread and wine, which would have been practically nonsensical not only in Abraham’s day but in the day of the Hebraist–but which points to the real sacrifice of Christ eventually. Catholics and High Protestants sure spend time and energy making this point! )