Create a scenario that has all the needed components for in-game testing or use a ready scenario that allows changing factions and also saving loadouts using Arsenal.

Switch to testing in-game: first select faction from the available ones and proceed to spawn. After spawning proceed to save the desired loadout.

Open the in-game menu and use Leave faction to change to the other available faction.

Observe that the loadout that was saved while on the previous faction is now available on the new faction.

See this video that I recorded using vanilla Arland Conflict for additional information. It shows the saving of loadout on one faction and loading the same loadout after changing to another faction on. Only modification the scenario shown in the video is that I have enabled changing of factions for the game mode.
https://www.youtube.com/watch?v=Iyv1L6uuNUs

In the video:

• allowing faction change for the game mode at 0:51
• saving loadout while on USSR faction at 2:28
• loading the saved USSR faction loadout after changing to US faction at 2:43
• saving loadout while on US faction at 4:23
• loading the saved US faction loadout after changing to USSR faction at 4:36