Libreoffice does not support at all the Republican calendar.
Use this page to document ways to support decimal time and the republican calendar in Libreoffice.
Fortunately, converting from and to decimal time is easy in Libreoffice.
Internally, Libreoffice saves times as a decimal number, with 1 being the value corresponding to a whole day, i.e. 24 hours.
If you have a field HH formatted as a time (24 hour clock), then you can have another field formatted as a number NN.
To convert 24 hour times to decimal time, use the formula: NN = HH * 10.