There are some debates about the details of calendar calculations among earlier Poskim about how to calculate the calendar, especially around pushing Rosh Hashana off deliberately.
For example, Hebrew Wikipedia records a divergence between R. Saadia Gaon and Ben Meir that cause a divergence for the years 4683 and 4684.
Did this type of argument ever cause different communities to actually have a different calendar, and thus have some holidays on a different day, for a given year, or were the disagreements only argued but never implemented? (I'm curious about the results on the ground of the 4683/4684 controversy as well: did that argument ever lead to actual divergent practices?)