> It was certainly not in Latin. It was either in Hebrew of in Greek.
I think it was very likely mostly Aramaic, possibly with some Hebrew mixed in (certain set prayers, with Torah readings in Hebrew followed by extemporaneous Aramaic translation). By the 1st century, Jews had abandoned Hebrew as an everyday tongue, a situation which didn't change until Zionists revived it in the late 19th century (which caused great controversy, since the traditional Jewish belief was that Hebrew is a holy language which should be reserved for religious purposes only, a position still maintained by most non-Israeli ultra-Orthodox to this day.)
Putting aside any claims of supernatural linguistic abilities, Jesus of Nazareth would likely have been fluent in Aramaic (his native tongue), competent in using Hebrew for certain religious purposes (but not as a language of everyday life), possibly some limited ability in Greek (but probably not fluent), maybe a few words of Latin (but very unlikely to be fluent).
> The focus on latin is a pure nitpicking and virtue signaling from the Conservatives (the irony!).
The majority of TLM (Traditional Latin Mass) adherents care more about keeping the traditional Tridentine (pre-Vatican II) liturgy than about Latin in itself – Catholic priests are allowed to say the contemporary Mass in Latin (subject to certain conditions), but there is rather little demand for it.