... from Brittanica: Semite, name given in the 19th century to a member of any people who speak one of the Semitic languages, a family of languages spoken primarily in parts of western Asia and Africa. The term therefore came to include Arabs, Akkadians, Canaanites, Hebrews, some Ethiopians (including the Amhara and the Tigrayans), and Aramaean tribes. Although Mesopotamia, the western coast of the Mediterranean, the Arabian Peninsula, and the Horn of Africa have all been proposed as possible sites for the prehistoric origins of Semitic-speaking populations, there remains no archaeological or scientific evidence of a common Semitic people. Because Semitic-speaking peoples do not share any traits aside from language, use of the term “Semite” to refer to the broad range of Semitic-speaking peoples has fallen out of favour. For this reason, some critics even encourage the removal of the hyphen in the term anti-Semitism to help dispel any pseudoscientific notions of a "Semitic race." They advocate instead for the use of antisemitism to describe the hostility toward or discrimination against Jews as a religious or racial group. In fact, by 2500 BCE Semitic-speaking peoples had already become widely dispersed throughout western Asia. In Phoenicia they became seafarers. In Mesopotamia they blended with the civilization of Sumer. The Hebrews settled with other Semitic-speaking peoples in Palestine.
Few if any words have only one meaning. I prefer the Britannica definition. But today "anti-semite" means "anti-jewish", apparently not in terms of religion, but, from the speaker's perspective, in terms of ethnicity or race. I suspect that "semite", too, is often used in that same restricted sense, but less so in academia and, obviously, britannica.
I don't claim to understand all the implications of it but there has been a long term serious conflict between secular and religious Jews. Jewish supremacy seems to come mainly from the secular side. Hitler regarded all the Jews as untermensch, roughly meaning 'less than men'. You would think that all Jews would take the lesson that this is wrong and not repeat it. Yet some Jews look for their own brand of it and to look for some people who they may look on as less than human. That role is filled by Palestinians. Do we learn nothing? I don't understand how the removal of a hyphen changes anti-semitism from prejudice against people who once spoke a brand of Semite language (including Arabs) to prejudice against only Jews. I suppose martyrdom cleanses one of all sin. The older I get the less I know.
The words Untermensch and Übermensch became propaganda tools, purposefully mistranslated and misinterpreted. Nietsche used the word Übermensch; I don't know whether the NSDAP/National-Socialists did. "Often misunderstood as a call for a superior human ‘race’, Nietzsche’s Übermensch is actually a call for personal self-discovery and self-overcoming." - Philosophy Break "An overman [übermensch] as described by Zarathustra, the main character in Thus Spoke Zarathustra, is the one who is willing to risk all for the sake of enhancement of humanity. In contrary to the last man [untermensch] whose sole desire is his own comfort and is incapable of creating anything beyond oneself in any form. ... [A]n overman has his own values, independent of others, which affects and dominates others' lives that may not have predetermined values but only herd instinct. An overman is then someone who has a life which is not merely to live each day with no meanings when nothing in the past and future is more important than the present, or more precisely, the pleasure and happiness in the present, but with the purpose for humanity." - https://ccrma.stanford.edu/~pj97/Nietzsche I don't know where "Herrenrasse" came from. Probably from Nietsche. I read that Hitler used "Herrenvolk" in Mein Kampf, only once, apparently in the sense of most advanced people, or the leading people (or civilization?). The switch from "Herrenvolk" to "Master Race" was probably due to language manipulators like Churchill and excuse-makers like William Shirer. Über- and Herren- as prefixes seem to have indicated a superior social position and view, not a physically, race-based superiority. As I currently understand the terms.
Being antisemitic would be a challenge for many, since the term is mostly used for the Jewish belief more so than race. Although there are several belief systems of the Jew. Some are total atheist, others real religious others somewhere in-between.