If the two terms (antisemitism and Islamophobia) had been coined at the same time and under similar circumstances, then obviously there would be reason to wonder why there is a use of “anti” in the one case and “phobia” in the other case. But, alas, the issue of the origin of the two terms is not analyzed in article.
“Antisemitism” was coined in the 19th century. The “logic” behind the term is that the Jews are the descendants of Shem (the son of Noah) whereas the Europeans are the descendants of Japhet (another son of Noah); hence, the Jews are “foreigners” in Europe. An antisemite, therefore, was one who objected to giving the Jews equal status in European society, based on the perception that the Jews are not Europeans. The term is racist by definition in that there is an objection to Jews because of their perceived descent (not because of their religion). Moreover, the term was invented by an antisemite (Wilhelm Marr).
“Islamophobia” is a term from the 20th century. The concept is meant to condemn those who object to believers in Islam; i.e. the term was not coined by an Islamophobe, and obviously it’s not about one’s perceived descent (“race”).
So, there’s no justification for drawing the conclusion that there is a “hierarchy of racism” in the two terms. That’s real nonsense. “Antisemitism” was a term that the antisemites themselves used with pride, whereas “Islamophobia” is not a term that the Islamophobes use in order to present their own agenda to the world. They are not parallel terms.