It's a bit of an impossible question without a time machine. But there's no record of a deliberate switch, and (to my knowledge) nothing indicating that two communities ever realized they were celebrating different days. Really it's not much different than asking about knowledge of days of the week in other societies, which (as far as I know) also was never an issue.

Because "probably not, but there's no way to prove it" isn't really a meaty answer, an additional note is that there were Reform Jewish communities in the 19th century, mostly in Germany but also in the US, that changed the Sabbath to Sunday. This was mostly to modernize Judaism by bringing it in line with contemporary secular norms, where secular society had Sunday as the designated day-off (before the modern 2-day weekend). This largely did not catch on, as it was from the more radical-reform leaning elements of Judaism. Even when the Sunday-only weekend caused lots of problems for the traditional Jewish world in the US, moving the Sabbath to Sunday was not accepted.