Your question is very broad. Let me address one aspect of it, namely interfaith dialogue with Christianity.
R Avraham Gordiner writes here
R. Moshe Feinstein, in a set of halakhic letters penned in 1967 to R.
Yosef B. Soloveitchik of Boston and to Dr. Bernard Lander (Igr. Moshe
YD 3:43-44), unequivocally forbade Jewish participation in ecumenical
dialogue with the Church, citing both concern for apostasy as well as
inherent prohibitions of such dialogue. R. Feinstein was firm as steel
that participation of any sort constituted grave infractions of
In a series of halakhic and binding policy correspondence between 1962
and 1967 (published in Community, Covenant and Commitment), R.
Soloveitchik articulated his unyielding position that Jewish
delegations should not and may not take part in religious discussion
with the Church. R. Soloveitchik expressed concern for apostasy and
wrote that the Jewish and Christian religious differences and world
outlooks are irreconcilable, such that discussion thereof would be
wholly unfruitful and would be wrong.
Although, unlike R. Feinstein, R. Soloveitchik maintained that in theory, dialogue with the Church about “humanitarian and cultural
endeavors” - universal, practical issues that do not touch upon
personal religious beliefs and practices - would be acceptable and
even positive (ibid. p. 260), the context of such dialogue in the
situations addressed by R. Soloveitchik caused him to prohibit Jewish
participation therein. R. Soloveitchik was adamant and unapologetic in
his refusal to allow any form of personal religious discourse between
Judaism and Christianity, and the circumstances and impressions
conveyed by even otherwise permissible interchange compelled him to
comprehensively ban such interchange in his correspondence.
See here for a foundational article by R Soloveitchik.
Specifically, as cited here R Soloveitchik writes
…We are, therefore, opposed to any public debate, dialogue or
symposium concerning the doctrinal, dogmatic or ritual aspects of our
faith vis a vis “similar” aspects of another faith community. We
believe in and are committed to our Maker in a specific manner and we
will not question, defend, offer apologies, analyze or rationalize our
faith in dialogues centered about these “private” topics which express
our personal relationship to the God of Israel. We assume that members
of other faith communities will feel similarly about their individual
We would deem it improper to enter into dialogues on such topics as:
- Judaic monotheism and the Christian idea of Trinity
- The Messianic idea in Judaism and Christianity.
- Jewish attitude on Jesus
- The concept of the Covenant in Judaism and Christianity
- The Eucharist mass and Jewish prayer service
- The Holy Ghost and prophetic inspiration
- Isaiah and Christianity
- The Priest and The Rabbi
- Sacrifice and the Eucharist
- The Church and the Synagogue – their sanctity and metaphysical nature, etc.
be mutual understanding concerning these topics, for Jews and
Christians will employ different categories and move within
incommensurate frames of reference and evaluation.
In May 2006, the Rabbinical Council of America restated these guidelines as applying regarding interfaith dialogue.
See also here for more sources.