It seems unlikely but I hope the Societists go for base six(senary) rationalised measurements as their universal system. Diversitarians certainly aren't going to near standardised measurements, and decimalisation smacks of Jacobin republics which is a massive turn-off for Societists.
(6^2)36 hours of 36 mins of 36 seconds results in hours, minutes, & seconds that are very similar to the current system. 1 s-hour = 40 real mins, 1 s-minute = 67 real seconds, 1 s-seconds = 1.85 real seconds. It wouldn't be nearly as jarring as decimal time. 365 days is also somewhat friendlier to senarisation than decimalistion, and 12 months looks more rational in senary than decimal. Maybe peg 6 special days in the year, and count how days until/past that special day it is (which actually works out to be 12 months of ~30 days + the 6 special days, so it's basically the normal calendar).
Maybe they'd take inspiration from Societist Kongo, since Congolese languages use senary number systems.
I wonder how the Societist will handle time zones. I would expect they'd just use on Universal time that all humanity abides to. And Societists would just get used to noon being whatever time noon happens to be where they are.
The issue is which latitude gets to have noon at noon? Zon1Urb1 probably couldn't get away with making it their latitude, but maybe they'll stick in the middle of the Atlantic Ocean so only an uninhabited patch of Greenland gets noon at noon, but it's also helpfully exactly 30 degrees ahead of Zon1Urb1 so their noon is only 3 s-hours/2 real hours off.