While Semitic these days is colloquially used to mean "Jewish" (mostly with the term "anti-Semitic), the Semites are actually people from a particular region of the Middle East. So both Middle Eastern Jews and Arabs are Semites. The Nazis must have known this, so how did they come to allow Arabs in the Waffen-SS? And subsequently, why would Hitler hold positive views of the prophet Muhammad?
Obviously cognitive bias can be very strong in some people (after all, why would you want to kill millions of people as they did), but this seems to be a large inconsistency in the Nazi ideology. Or is there an aspect of their beliefs of which I am unaware?
They weren't trying to kill of Semitic peoples, they were trying to commit genocide against the Jews.
While "Semitic" is and was a term describing some more middle eastern peoples, "Anti-Semitism" has been a term specifically for anti-jewish prejudice and hatred. As early as in 1865, the term Anti-Semitismus was described as opposition to things typically perceived as "jewish" by the official dictionary of Prussia. The german journalist Wilhelm Marr later made the term more popular by publishing the "Antisemitische Hefte", a journal, and founding the "Antisemiten-Liga", the League of Antisemites. By using this term, Marr and his followers tried to distance themselves from the old, religious anti-judaism and make it look more scientific, "enlightened" if you will.
To sum it up: It was never about "Semites", it was always about Jews.
Do you have any evidence that Arabs joined the Waffen SS?