I tried using BIS_fnc_setUnitInsignia on a modded dedicated server, with 2 clients.
There were inconsistent synchronisation problems.

If a small sleep could be implemented as indicated in setObjectTextureGlobal (comment 2), it would most likely address the problem (I have tested a version with a delay of 0.1 s and the issues went away).

Additionally, if BIS_fnc_setUnitInsignia could set the desired insignia on the first try (instead of having to clear it first, then setting it: See BIS_fnc_setUnitInsignia, comment 2), that would be nice.