Antisemitismus is the only attested way to phrase it:
Praeterea, Ecclesia, quae omnes persecutiones in quosvis homines reprobat, memor communis cum Iudaeis patrimonii, nec rationibus politicis sed religiosa caritate evangelica impulsa, odia, persecutiones, antisemitismi manifestationes, quovis tempore et a quibusvis in Iudaeos habita, deplorat
- The Vatican, which usually prefers noun phrases not new words in Latin
"Judeomisia" is a fabrication by uneducated English speakers trying to sound smart. There are no educated attestations in Google Scholar. English is freer in terms of "constructed backwards." However, I found no "-misia" suffix in Greek. It is always "miso-" and even that affix isn't productive. Even the "Judeo-" prefix isn't very productive in Greek (1 2 3 4). Classical Latin does not like you creating new words, and Neo-Latin won't understand you if new nouns diverge from English too much. Greek possibly to a lesser degree likewise. It's unlike English words from Greco-Latin. I would either use an established word or a noun phrase. "Islamophobia" is well-formed by itself. Not all languages, especially ancient languages, make the conceptual distinctions we do today in English like if a word "suggests fear" or "suggests hate."
Modern Wikipedia has Antisemitismus, Islamophobia, Αντισημιτισμός, and Ισλαμοφοβία. If there was an established alternative term, there would have been redirects, but there are none (1 2 3 4).
You could also use a noun phrase like odium in iūdaeōs and odium in musulmānōs. Both odium in and odium contra are the most natural. After all, we went centuries saying "the world hating the disciples" without inventing words like "theophobia." If anything, noun phrases feel the least recent.