Semitic comes from Shem who was one of the three sons of Noah from which all of humanity issued.
Abraham was the 7th great-grandson of Shem. From Abraham comes the Jews (Isaac) and the Arabs (Ishmael), so they are semites.
Lot was Abraham's nephew so he was a semite. From Lot came the nations of Ammon and Moab ( Jordan) so all those people are semitic.
So, the use of the word Anti Semitic to talk about hating Jews is wrong.
To truly be Anti Semitic one would have to hate Jews and Arabs including the Jordanians.
Not to believe that Jews are the Chosen People is not the same as being antisemitic. Antisemitism is based on hate.
It is wisdom to understand that the Chosen People are those who respond positively to The Call of the Holy Spirit Of Christ Jesus upon hearing the Gospel.
Jesus fulfilled the calling of Abraham doing away with the flesh.
Jesus fulfilled the Law doing away with works.
The New Covenant is based on Grace Through Faith that Christ is the risen Lord, Savior, Mighty God and King of all.