I am originally from Savannah, GA, an American and Israeli citizen since 1975. I belong to St. Anthony parish in Jaffa and St. Peters Church, a Franciscan shrine also holds mass in Hebrew in the chapel. Saturday evening mass has about 30 congregants and they are mostly Hebrew speaking Russian immigrants. In Jerusalem they are mostly French. The whole community is between 400 and 600 congregants. Those that are Jewish according to Halacha are very small. In Israel since the Yom Kipper (1973) war there has surfaced a growing movement of mostly evangelist Jewish converts to Christianity (Messianic Jews) that number between 16,000 to 20,000. Some try to make a synthesis between Judaism and Christianity in traditions observed. The issue of Jew converting to Christianity is contentions to say the least and Christianity is held in suspicion. Even though is below the radar of most Israelis, Hebrew Catholics and Messianic Jews have lively communities.
In the 1950’s the pope granted mass to be said in Hebrew in Israel prior to Vatican II, most Hebrew speaking Catholics were French and Polish. The mass and traditions are that of the Roman rite. Attempts to create a Hebrew rite have essentially died out.
The attitude of most is integrating into Israeli society and to be Catholic. Whatever attitudes they may have toward Judaism it would be like that of Secular Jews.
The Arab catholic community in Jaffa does not want anything to do with Hebrew Catholics and do not want their mass held at St. Anthony church their church. St. Anthony does have masses in English for the foreign workers (Filipinos, Africans and Indians) but even here there is tension.
From what I’ve read from Internet, the Hebrew Catholic communities in the U.S are much larger and have fewer restraints. I myself, even though in Israel I am legally registered in the Ministry of the Interior as Jewish and have at one time practiced Ultra Orthodox Haradi (from the Hatzer of the Rebbi of Krechnev from Rehovot) Judaism, I have not tried to make a bridge between the two worlds because it is simply impossible and too much emotionally charged to attempt. Even though they are both from the same roots, they are worlds apart; they are 2 very different and separate civilizations. The feeling is that you are part of an underground church like in China.