Its well documented that Romans would absorb religions and religious ideas from other cultures while 'Romanizing' them for domestic consumption This was the case with almost every culture they had contact with - and even the ones they didn't.
The glaring exception to this seems to be the Jewish faith. (Correct me if I'm wrong but) there's almost no example of syncretism towards the Jewish religion or any of its concepts even though Romans had been in contact with Judaism for centuries.
In my previous posting of this question, someone did reply [it got auto-deleted afterwards] that Judaism's monotheism didn't appeal to the Romans as well as the thousands of Talmudic laws but also its strict dietary laws.
Yet this does not answer why absolutely no attempts were made at syncretism at all, after all Roman versions of appropriated religions often bore little resemblance to their point of origin anyway.
For example why don't we ever see something like a 'Cult of Abraham' or 'Cult of David' that has no resemblance to the main Jewish faith but clearly has its origins within it?
Is it possible something like this DID exist but has since been lost or evidence of it remains buried deep underground and since forgotten?
Or was there maybe some sort of formal agreement amongst Jews and Romans that the Jewish religion would be left alone and not appropriated in any way?
There were actually was some degree of syncretism and observance of Jewish customs among goyim (Greeks, Romans, etc.) both in Palestine and in proximity to Jewish groups in exile (especially Greece, Syria, Italy, Spain, and North Africa).
They’re referenced in Christian, Jewish, and Graeco-Roman texts as “God Fearers” or “God Worshippers” (yir’ei Hashem/ theosebeis) who claimed worship Hashem and abided by the 7 laws of Noah (Don’t worship idols; Don’t curse Hashem; Don’t commit murder; Don’t commit adultery and other sexual immorality; Don’t steal; Don’t eat from a living animal; Establish courts to administer justice). Some would follow other Jewish customs, such as certain dietary laws or even Shabbat ,but would not convert. Very few would undergo circumcision and full conversion (gerim tzedekim “righteous foreigners”)z By following the 7 laws of Noah, they fulfilled the religious obligations of a non-Jew and we’re not obligated to convert.
Judaism’s monotheism is actually what attracted the majority of these people, and although the Greeks and Romans discriminated against Jews throughout their histories, many philosophers they respected the ancient spirituality of Jewish monotheism. The main aversion to Judaism were the extensive restrictions (613 laws in the Torah), however the Talmud was not yet fully compiled until the 4th-6th centuries (kinda out of the scope of this question).
There’s generally a lot of confusion about the Talmud. The Talmud is a compilation of hundreds of years of Rabbinical writings, stories, and legal decisions written in multiple parts, mainly in the Galilee and Mesopotamia. It was mainly meant as a guidebook of “proper” Jewish practices, after the Sanhedrin, Temple, and main Jewish courts in Israel were destroyed and as the Jews went into exile across Afro-Eurasia.
What attracted many of these “God Fearers” was probably the mystical Rabbis who influenced the Talmud, and the Hellenistic synagogues in the diaspora which served more as social and legal discussion places than the more religious function they currently have.
It is not known how many people held these beliefs and followed what rites / traditions/ practices, and many likely participated in secret or participated alongside Pagan rituals.
However, it is thought that these pagans sympathetic to Jewish monotheism, along with Jews in the diaspora - heavily affected by Hellenistic ideas - were the main early converts and missionaries of Christianity: the largest, most influential, obvious, and long lasting example of Greco-Roman religious “appropriation” (as you put it, I would not phrase it that way as that word has somewhat of a negative connotation)
I am not an expert on Roman religion but I am quite knowledgable on the history of Thessaloniki which can provide an example of Roman syncretism. Hopefully this specific example does comply with the rules since it answers a specific question posted by the poster and Thessaloniki being a major roman city does provide enough "weight".
Jewish presence at roman Thessaloniki can be traced at least back in 50CE when Apostotle Paul visited an already established vibrant community. But our main sources are the inscriptions of that era which point to two Jewish communities, the rabbinic and the Samaritan one with multiple synagogues prominent enough (1) and a third community which is described by scholars arbitralily as Savvatistes or Σεβομένων τον Θεο (Respectful of God).
These are not to be confused with the Maamin/Donme sect of Sabbetai Sevi and take their name from the prolific use of the name Savatios/Samvathe/Samvo and similar. They adopted many Jewish customs, principally the Shabbath as a day of rest, but fell short of converting all together with most important hurdle the acknowledgment of the divine aspects of the Emperor. Of course this is an assumption based on the presence of both Jewish and non-Jewish names in tombstones like Δομέτιος ω και Βενιαμήν in a cubiculum grave which survived the destruction of the Jewish cemetery by the Greek state, the biggest Jewish cemetery in Europe by the 1950's. Still one cannot be certain since in the case of the sarcophagus of Αυρήλιος Σαββατιος of the 2nd century CE found in the Archeological Museum may indicate both acceptance of the divine emperor or simply the emperor ruling when he acquired roman citizenship.
Although liberal frequentation between these groups is known, later mirrored in the common frequentations/meals between early Christians and Jews, we know litle of them. The abundant presence of variations of names based on Shabbath, not really popular among rabbinic or Samaritan Jews, points to their presence but this is as far as one can go.
So, while we know litle about this group there is clear evidence that a third distinct community existed in Thessaloniki which developed a distinct Roman path to Judaism whole retaining Roman elements in a syncretistic way.
Main sources is Nigdelis Επιγραφικα Θεσσαλονίκεια which is an extended commentary on the inscriptions found in Thessaloniki. Although litle work has been done on the subject, tangentially it has been touched by Devin Naar, Jecky Benmayor, Iacov Sciby and Iosif Vaena.
(1) the term prominent is justified because they are used as the destination of the apotreptic fines written on the sarcophagus, should it be violated. In non- Jewish tombs the city's vault is used in their place.