My Skyrim MO works fine when switching between profiles, and uses similar programs in much the same way (CK vs GECK, TESVEdit vs FNVEdit, etc) so I don't think it's a matter of being installed incorrectly. I'm not sure how you are using profiles and what you expect with different profiles. Any executable you run will see the plugin load order for the currently selected profile, and if you change to a different profile that has a different load order then the executable will see a different load order. If you change the plugin load order in the first profile (e.g., by running LOOT or BOSS), the plugin load order in the new profile will not get the new changes. If you change the priority of a mod in the first profile, the new profile won't have this change to the mod's priority. At the time you created the new profile the mod installation order and the plugin load order in the two profiles are exactly the same. You can 'Copy' that profile to a new profile and give the copied profile a new name (e.g., Profile2). You can, for example, create an MO profile (e.g., Profile1) and then organize the profile priorities in the left pane (mod installation order) and the plugin load order in the right pane. That isn't how profiles work in Mod Organizer they are independent. You seem to be expecting changes in one Mod Organizer profile to automatically be applied to the mods and plugins in another Mod Organizer proflle. Obviously this is a huge problem that will cause instability within saves if the load order keeps changing. Esm's are jumbled around and moved to the bottom of the esm portion of the load order and some esp's are moved to the top of the esp portion of the load order. When I switch to a different profile and launch any executable with that profile, be it the GECK, FNVEdit, or the game itself, the load order on my main profile is scrambled.

Morrowind load order sorter