Though I am Jewish, I have some family who are Hebrew Catholics.
While the Catholic Church encourages all to research Christianity’s Jewish heritage, it does not encourage Christians who are not of Hebrew heritage to join the Hebrew Catholic movement. The reason is that the practices involved are meant for the preservation of those who are from a Jewish background, and that there are specific Church laws discouraging non-Jewish Catholics from engaging in Jewish practices without proper training in Jewish liturgy.
For instance the USCCB states regarding Christians attending or holding a Seder:
It is wrong…to “baptize” the Seder by ending it with New Testament readings about the Last Supper or, worse, turn it into a prologue to the Eucharist. Such mergings distort both traditions…Christians who wish to attend a Passover Seder should do so at the invitation of Jewish friends, families or synagogues that often welcome guests to this important meal. This allows Christians to experience the Seder as a Jewish family liturgy…However, in the event that Christians celebrate the Seder alone…the rites of the haggadah for the Seder should be respected in all their integrity.
While the Hebrew Catholics won’t turn you away, it is not meant to be an alternative group for people who wish to join the Catholic Church
with a “Jewish” feel. It is for Roman Catholics of Jewish descent who wish to keep their cultural practices alive within the boundaries of the Church. Members of the Hebrew Catholic community are already generally well-trained in Jewish liturgy and Hebrew because they are
already Hebrew and of Jewish descent.
While I do not discourage your converting to Catholicism or looking into the Hebrew Catholics, I would take on one at a time. I would concentrate on just converting to Catholicism. If you feel God calling you to the Catholic Church, then let God do God’s work on bringing you there. There’s enough in common with Judaism within the Church as it is that you don’t need to belong to the Hebrew Catholics to experience a rich tradition or connection with Israel through that group. It’s there in the Catholic Church, and I say that as a practicing and a Torah-observant Jew.
If, as you study to become a Catholic, you still feel a call to Judaism, I would talk to your sponsor or a catechist, or with a priest. Perhaps God is not calling you to the Church. But don’t make any rash decisions just yet. Talk it over with some people. Or maybe try another form of Judaism than the one you tried before, but stay on the road you are for now and go from there before changing your mind. People in the Catholic Church will help guide you either way.