I'm having the same issue. It's really confusing too because the unit selection boxes don't line up with the soldiers. I was really confused when I clicked on the loadout for my Specialist and got the loadout for my Sharpshooter. I'll just have to pay more attention to the names and classes.

You should be able to see all 8 unit loadouts, but not the units themselves.

If you want to actually see all 8 units, try Robojumper's Squad Select, a new squad select screen which also lines up the boxes with the soldiers.

You will need to set "squad select screen" to "compatibility mode" in this mod's Mod Config Menu options.